Question

The function f(x)=125(0.9)x models the population of a species of fly in millions after x years.

Answer 1

Answer: (B) 3 times as fast

Step-by-step explanation:

rate of change is the "slope" between the given interval.

f(x) = 125(.9)ˣ

f(1) = 125(.9)¹

    = 112.5

f(5) = 125(.9)⁵

     = 73.8

$\dfrac{f(5) - f(1)}{5 - 1} = \dfrac{73.8-112.5}{5-1} = -\dfrac{38.7}{4} = -9.675$

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f(11) = 125(.9)¹¹

       = 39.2

f(15) = 125(.9)¹⁵

       = 25.7

$\dfrac{f(15) - f(11)}{15 - 11} = \dfrac{39.2-25.7}{15-11} = -\dfrac{13.5}{4} = -3.375$

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The rate of change from years 1 to 5 is approximately 3 times the rate of change from years 11 to 15.