Home / Assignment Help / In Texas, the population of a species of bats is decreasing at a rate of -0.121 per year. The population was 34,000 in 2000. According to the function; A(t) = A0e^(kt), what is the predicted population in 2015?

In Texas, the population of a species of bats is decreasing at a rate of -0.121 per year. The population was 34,000 in 2000. According to the function; A(t) = A0e^(kt), what is the predicted population in 2015?

Answer:

Population of bats in year 2015 is 5536.

Step-by-step explanation:

The given function A(t) = A_{0}e^{-kt} predicts the population of bats after t years.

Here A(t) = population after ‘t’ years

           k  = growth constant

           t = time in years

          A_{0} = initial population

In year 2000 population of bats A(t) = 34,000

Since rate of decrease in population k = 0.121 per year

So population in 2015 will be

A(t) A_{0}e^{(-0.121)(15)}

= 34,000 [ e^{-1.815} ]

= 34,000 ( 0.162837)

= 5536 bats

Therefore, population of bats in year 2015 is 5536.

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