Question

The function f(x)=60(1.5)xf(x)=60(1.5)x models an animal population after x years.

How does the average rate of change between Years 3 and 6 compare to the average rate of change between Years 0 and 3?

The average rate of change is 1.5 times as fast.

The average rate of change is 3 times as fast.

The average rate of change is 3.375 times as fast.

The average rate of change is 2.25 times as fast.

Answer 1

C.The average rate of change is 3.375 times as fast.You add them up and subract

Answer 2

Answer:

The average rate of change is 3.375 times as fast.

Step-by-step explanation:

The given function is $f(x)=60(1.5)^x$

The average rate of change of a function f(x) is given by

$\frac{f(b)-f(a)}{b-a}$

Thus,  average rate of change between Years 3 and 6 is given by

$\frac{f(6)-f(3)}{6-3}\\\\=\frac{\left(60\left(1.5\right)^6-60\left(1.5\right)^3\right)}{3}\\\\=160.3125$

Now, average rate of change between Years 0 and 3

$\frac{f(3)-f(0)}{3-0}\\\\\frac{\left(60\left(1.5\right)^3-60\left(1.5\right)^0\right)}{3}\\\\=47.5$

The ratio of these average rate of change is given by

$=\frac{160.3125}{47.5}\\\\=3.375$

Therefore, the average rate of change is 3.375 times as fast.