Question

Terry invested money in a biotech stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents number of days. Find the approximate average rate of change from day 2 to day 10.

Answer 1

The average rate of change is 1.275

Answer 2

The average rate of change is 1.275

Explanation:

The average rate of change of f(x) from x=a to x=b is given by:

`(f(b)-f(a))/(b-a)`

The money Terry invested is modeled by the function
`f(x)=0.01(2)^x` where x represents number of days.

The average rate of change from day 2 to day 10 is given by:

`(f(10)-f(2))/(10-2)`

`f(10)=0.01(2)^(10)=10.24`

`f(2)=0.01(2)^(2)=0.04`

The average rate of change becomes:

`(10.24-0.04)/(8)`

`=(10.2)/(8)=1.275`