contestada

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.

Respuesta :

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  [tex]f(t) = 110(1.35)^{\frac{t}{40} }[/tex]

By comparing with the form  [tex]f(t) = ae^{kt}[/tex] , we get

a = 110.0000

k = [tex]\frac{1}{40}[/tex] = 0.0250

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