Question

All exponential functions can be written in many forms. Write the function f(t)=110(1.35)^{\frac{t}{40}}f(t)=110(1.35) 40 t ​ in the form f(t)=ae^{kt}f(t)=ae kt . Round all coefficients to four decimal places.

Answer 1

Step-by-step explanation:

Given - f(t)=110(1.35)^{\frac{t}{40}}

To find - Write the function in the form f(t)=ae^{kt}. Round all coefficients

               to four decimal places.

Proof -

Given that , the function is  f(t)=110(1.35)^{\frac{t}{40}}

Now,

We can write it in the form of  $f(t) = 110(1.35)^{\frac{t}{40} }$

By comparing with the form  $f(t) = ae^{kt}$ , we get

a = 110.0000

k = $\frac{1}{40}$ = 0.0250