Question

Find the exponential function that satisfies the given conditions: Initial value = 33, increasing at a rate of 7% per year (2 points)

Answer 1

`f(x)=33*(1.07)^x`

Explanation:

Let f(x) be our exponential growth function representing growth after x years.

We are asked to find the exponential function that satisfies the given conditions: Initial value = 33, increasing at a rate of 7% per year.

Since an exponential growth function is in form:
`y=a*(1+r)^x`, where a= initial value of function and r = growth rate in decimal form.

Given:

a=33

r=7%.

Let us convert our given rate in decimal form.

`7\text{ percent}=(7)/(100)=0.07`

Now let us substitute our given values in exponential function form:

`f(x)=33*(1+0.07)^x`

`f(x)=33*(1.07)^x`

Therefore, the exponential function that satisfies our given conditions will be
`f(x)=33*(1.07)^x`.