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

Answer:

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

Step-by-step 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.

$7\text{ percent}=\frac{7}{100}=0.07$

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 $f(x)=33*(1.07)^x$.