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Given the exponential equation 2x = 128, what is the logarithmic form of the equation in base 10?

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Answer:

log_{2}128= frac{log_{10} 128}{log_{10} 2}.  

Step-by-step explanation:

Given : 2^{x} = 128.

To find :  what is the logarithmic form of the equation in base 10

Solution : We have given that 2^{x} = 128.

By th change base rule ( inverse of exponential function )

a^{b} = c is equal to  log_{a}(c) = b

Then 2^{x} = 128 in to logarithm form  log_{2}(128) = x.

Then in to the base 10 logarithmic form.

By the change of base formula log_{b}a= frac{log_{10} a}{log_{10} b}.

Then , log_{2}128= frac{log_{10} 128}{log_{10} 2}.  

Therefore, log_{2}128= frac{log_{10} 128}{log_{10} 2}.  

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Simplify the expression in exponential notation. 2 • a • b • a • b

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Simplify the expression in exponential notation. 2 • a • b • a • b

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From the table below, determine whether the data shows an exponential function. Explain why or why not. (x) -5, -4, -3, -2 (y) 0.5, 2, 8, 32 A) Yes; the domain values are at regular intervals and the range values have a common factor 8. B) Yes; the domain values are at regular intervals and the range values have a common factor 4. C) No; the domain values are not at regular intervals. D) No; the domain values are at regular intervals and the range values have a common factor 4. Please help, and please give me an explanation on the answer you choose because I need to make corrections. Please.

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Answer:

Option B-  Yes; the domain values are at regular intervals and the range values have a common factor 4.

Step-by-step explanation:

Given : The data

(x) -5,   -4,  -3,   -2

(y) 0.5,  2,   8,   32

To find : The data shows an exponential function or not

Solution :

The general form of an exponential form is y=ab^x

To check whether the data give the exponential function we form equation with the help of two points and verify the other two points .

y=ab^x

Let x= -5 and y=0.5

0.5=ab^{-5}

frac{0.5}{b^{-5}}=a ……[1]

Let x= -4 and y=2

2=ab^{-4}

frac{2}{b^{-4}}=a ………[2]

Equate LHS because RHS is equal in equation [1] and [2]

frac{2}{b^{-4}}=frac{0.5}{b^{-5}}

frac{b^{-4}}{b^{-5}}=frac{2}{0.5}

b=4

Put back in [2]

frac{2}{4^{-4}}=a .

a=2times4^4

a=2times256=512

a=512 and b=4

Exponential function – y=4(512)^x

To verify this function put

1) x=-3

y=512(4)^{-3}

y=farc{512}{64}

y=8

The point satisfied.

2) x=-2

y=512(4)^{-2}

y=farc{512}{16}

y=32

The point satisfied.

Therefore, The given data is an exponential function y=4(512)^x

The domain values are at regular intervals and the range values have a common factor 4 because b=4 and the change happen but value of b remain same.

Hence, Option B is correct.

Yes; the domain values are at regular intervals and the range values have a common factor 4.

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The function y = 4x is an exponential growth function. The graph of the function increases as x increases. The variable x is a(n) coefficient term exponent factor

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The function y = 4x is an exponential growth function. The graph of the function increases as x increases. The variable x is a(n) coefficient term exponent factor

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Analyze the characteristics of exponential and logarithmic functions. Make sure you talk about domain and range. Compare them to other functions.

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Analyze the characteristics of exponential and logarithmic functions. Make sure you talk about domain and range. Compare them to other functions.

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A function is shown below: f(x) = (0.07)x What does the function represent? Exponential growth of 7% Exponential decay of 7% Exponential growth of 93% Exponential decay of 93%

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Answer:

Exponential decay of 93%

Step-by-step explanation:

A function is shown below:

f(x) = (0.07)^x

Exponential formula is

f(x)= a(1+r)^t

r is the rate of growth or decay

From the given f(x) , we have 1+r = 0.07

Subtract 1 from both sides

r= 0.07 -1

r= -0.93

To get % we multiply by 100

r= -93%

the value of ‘r’ is negative , so its exponential decay

Exponential decay of 93%

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If Denise wanted to create a function that modeled an exponential function with base of 12 and what exponents were needed to reach specific values, how would she set up her function? f(x) = x12 f(x) = log12x f(x) = 12x f(x) = logx12

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Denise creates the exponential function g(x)=12 ^{x}

assume she want to find for what value of x, her function reaches the value, 3, or 8.2, or any value a (larger than 0)

so she shants to solve 12 ^{x}=a   (“for what value of x, is 12 to the power of x equal to a?”)

this expression is equivalent to x=log_1_2(a)

(so 12 to the power of x is a, for x=log_1_2_(a))

we can generalize this result by creating a function f.

In this function we enter x, the specific value we want to reach. f will calculate the exponent needed, in the following way:

f(x)=log_1_2(x)  

(example: we want to calculate at which value is  12^{x} equal to 5?
answer: f(x)= log_1_2(5),

check: 12^{log_1_2(5)} =5, which is true, by properties of logarithms)

Answer: log_1_2(x)       (B)

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A country’s population in 1992 was 72 million. In 1998 it was 76 million. Estimate the population in 2012 using the exponential growth formula. Round your answer to the nearest million.P=Ae^kt

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You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

 = 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.

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Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.

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Which type of function is represented by the table of values below? x y 1 4 2 16 3 64 4 256 5 1,024 exponential linear quadratic square root

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Answer:

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

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Identify the domain of the exponential function shown in the following graph: y=10x

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Answer:

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

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The graph of an exponential function is a curved line that increases or decreases True False

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The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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Graph the functions and approximate an x-value in which the quadratic function exceeds the exponential function. y = 4x y = 7×2 + 4x – 2

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Answer:

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

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A "b" value of less than 1 produces a graph with an exponential decay.

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A “b” value of less than 1 produces a graph with an exponential decay.

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Represents a exponential form – AnswersMine

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The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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Find the exponential function that satisfies the given conditions: Initial value = 70, decreasing at a rate of 0.5% per week

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127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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According to the yerkes-dodson law, the relationship between arousal and performance can be described by a(n) ____.? a. ?positive linear function (more arousal leads to better performance) b. ?positive exponential function (more arousal leads to better and better performance; a lot of arousal leads to tremendously good performance) c. ?inverted u-shaped function (more arousal leads to better performance, but only up to a point; too much arousal can hinder performance) d. ?negative linear function (less arousal leads to better performance)

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Answer:    Joshua is correct

Explanation:  Animals, however well preserved and bred in conditions that are not in nature, that is, not in their natural habitat, animals still retain the animal instinct. Thus, young animals in the wild can be met daily, except for members of their species, and members of all other species, including predators, as well as humans. This means that in the natural environment, young animals can find themselves in a variety of dangers on a daily basis, but not only that. In this way young animals develop their ability to survive, escape from predators, manage, and develop their hunting skills, etc. All this is essential for socialization because according to all these developed skills and abilities their socialization depends. To deny any of the conditions prevailing in the wild means to deny the development of any skill or instinct, to deny proper socialization.

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A radio active isotope decays according to the exponential decay equation where t is in days. Round to the thousandths place. For the half life: The half life is the solution (t) of the equation : a2=ae−7.571t a 2 = a e − 7.571 t

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You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

 = 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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Find the missing value for the exponential function represented by the table below. x y -2 26 -1 18.2 0 12.74 1 2 6.2426 a. -8.918 b. 9.213 c. 8.756 d. 8.918

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Find the missing value for the exponential function represented by the table below. x y -2 26 -1 18.2 0 12.74 1 2 6.2426 a. -8.918 b. 9.213 c. 8.756 d. 8.918

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Find the missing values for the exponential function represented by the table below. xy -2 4 -1 6 0 9 1 2 a. -13.5 -20.25 c. 6 4 b. -13.5 20.25 d. 13.5 20.25

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Answer:

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

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Find the missing value for the exponential function represented by the table below. x y -2 26 -1 18.2 0 12.74 1 2 6.2426 a. -8.918 c. 8.756 b. 9.213 d. 8.918

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Find the missing value for the exponential function represented by the table below. x y -2 26 -1 18.2 0 12.74 1 2 6.2426 a. -8.918 c. 8.756 b. 9.213 d. 8.918

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Select the types of models that can be used to predict a set of data. Select all that apply. linear quadratic cubic exponential

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Answer:

Ques 1)

           The lower quartile for the data.

Ques 2)

             99 points

Ques 3)

 There are exactly 3 students with 4 pairs of shoes.

Step-by-step explanation:

Ques 1)

Minimum value=40

Maximum value=120

First quartile or lower quartile (i.e. Q_1 ) =57

Third quartile or upper quartile (i.e. Q_3 )=112

Median (i.e. Q_2 )=88

The information that is provided by the box plot is:

          The lower quartile for the data.

Ques 2)

The scored earned by Theresa in four test are:

88 points, 84 points, 88 points, and 91 points

Let ‘x’ be the point she earned in the fifth test.

Hence we need to find ‘x’ such that the average score is 90 points.

i.e.

dfrac{84+88+88+91+x}{5}=90\\\84+88+88+91+x=90times 5\\\351+x=450\\\x=450-351\\\x=99

Hence she scores 99 points in the fifth test.

Ques 3)

              Pair of shoes           Number of students

                       1                                   1

                       2                                  3

                       3                                   5

                       4                                   3

                        5                                   1    

Hence, the dots above the number 4 indicate that:

    There are exactly 3 students with 4 pairs of shoes.

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Which is an exponential decay function? f(x) = 0.2(5/3)^x f(x)=-3.1^x f(x)=10^x f(x)=-2(0.7)^x

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1. Consider the function y=f(x), the x-intercepts are the values of x for which f(x)=0

2. So an x-intercept has coordinates (x,0)

3. If (0, 0) is an x- intercept, then f(0)=0
    If (4, 0) is an x- intercept, then f(4)=0

4. Check: 

a. f(x) = x(x − 4)

f(0)=0(0-4)=0,
f(4)=4(4-4)=4*0=0

so f(x) = x(x − 4) has x intercepts at (0,0) and (4,0)

b. f(x) = x(x + 4)
    f(0)=0*(0+4)=0 but f(4)=4(4+4)=4*8=32, so not 0

 c. f(x) = (x − 4)(x − 4)
     f(4)=(4-4)(4-4)=0
     f(0)=(0-4)(0-4)=(-4)(-4)=16 so not 0

d. f(x) = (x + 4)(x + 4)
    
f(0)=(0+4)(0+4)=4*4=16 so not 0

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What would occur if exponential growth occurred in a population

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Ans.

Plant hormones are signalling molecules, produced b plants that regulate growth, development and other cellular processes of plants. There are five types of plant hormones, which include abscisic acid, auxins, cytokinins, ethylene, and gibberallins.

Given chart represents relationship between different plant hormones and their responses or functions. Auxin promotes plant growth, plays role in tropism, abscisic acid plays role in seed and bud dormancy, cytokinin promotes cell division, ethylene controls plant growth and stimulates flowering, and gibberallins cause stem elongation.

Thus, the correct answer is option (B).

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Which of the following can be modeled with an exponential function? Select all that apply. A. Height over time that a football is thrown across the field. B. The cost to attend Universal Studios increases by 1% each year. C. An endangered species population is decreasing by 12% each year. D. The distance a bicyclist travels when cycling a constant speed of 25 mph. E. The population of a town that is growing by 5% each year.

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Answer:  The answer is (B), (C) and (E).

Step-by-step explanation: We are given five options out of which we are to select all those which can be modelled by exponential functions.

We can see that the options (A) and (D) cannot be modelled by exponential functions, because the rate of increasing or decreasing are not calculating compoundly.

But, in options (B), (C) and (E), the rate is increasing or decreasing each year.So, these three can be modelled by exponential functions.

In fact, the options (B) and (E) will show exponential growth because the number is increasing and option (C) will show exponential decay as the number is decreasing.

Thus, (B), (C) and (E) are the correct options.

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