SOLUTION: Convert the equation f(t) = 116(0.69)^t to the form f(t) = ae^kt Find a = ? and k = ? Round off to three decimal places

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Question 1204990: Convert the equation f(t) = 116(0.69)^t to the form f(t) = ae^kt
Find a = ? and k = ?
Round off to three decimal places

Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

to

....=>
.....take log of both sides


......substituting , then dividing by , we have


,




Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

a = 116 since it's the coefficient out front.
Alternatively, plug in t = 0 to find f(0) = 116 in the first equation and f(0) = a in the second equation. That leads to a = 116.


rewrites to
The base is
Set this equal to the base 0.69 and isolate k.


approximately


Summary
a = 116
k = -0.317 approximately

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