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**Answer:**

Maureen’s body eliminated the antibiotic faster than Ken’s body.

**Step-by-step explanation:**

To find the rate at which Maureen’s body uses the antibiotic, we find the percent of change. To do this, we use the formula

Between hour 1 and hour 2, the amount of change was 150-90 = 60. The “original amount” between these two is 150; this gives us

60/150 = 0.4

Between hour 2 and hour 3, the amount of change was 90-54 = 36. The “original amount” was 90; this give us

36/90 = 0.4

Between hour 3 and hour 4, the amount of change was 54-32.4 = 21.6. The “original amount” was 54; this gives us

21.6/54 = 0.4

Between hour 4 and hour 5, the amount of change was 32.4-19.4 = 13. The “original amount” was 32.4; this gives us

13/32.4 = 0.40

Her body had 100%-40% = 60% of the antibiotic remaining after each hour.

We can analyze Ken’s function to see how much his body used. His function is of the form

f(x) = a*bˣ,

where a represents the original amount, b represents 1 + the rate of change, and x represents the amount of time.

In place of a in Ken’s function, we see 200; this is the amount he was originally given.

In place of b, we see 0.976; this means we have subtracted something from 1:

1-0.976 = 0.024

Ken uses 0.024 = 2.4% of the antibiotic per hour.

Maureen uses it up more quickly.

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