Respuesta :
Answer:
[tex]f(x)=33*(1.07)^x[/tex]
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: [tex]y=a*(1+r)^x[/tex], 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.
[tex]7\text{ percent}=\frac{7}{100}=0.07[/tex]
Now let us substitute our given values in exponential function form:
[tex]f(x)=33*(1+0.07)^x[/tex]
[tex]f(x)=33*(1.07)^x[/tex]
Therefore, the exponential function that satisfies our given conditions will be [tex]f(x)=33*(1.07)^x[/tex].
