How do you rewrite y=−8(1.589)^(t−3) in y=A_0e^(at) form for appropriate constants A_0 and a? For other problems I took the ln of the number inside the parenthesis. So for example I would've done y=−8ln(1.589)^(t−3) then I would get the answer y=−8(e^(0.46317−3)) but that is wrong on my assignment. What do I do with the −3? I tried multiplying it by the −8 to get 24 but that isn't right either.

Melissa Walker

Melissa Walker

Answered question

2022-11-11

Rewriting in y = A 0 e a t
How do you rewrite y = 8 ( 1.589 ) t 3 in y = A 0 e a t form for appropriate constants A 0 and a ?
For other problems I took the ln of the number inside the parenthesis. So for example I would've done
y = 8 ln ( 1.589 ) t 3
then I would get the answer
y = 8 ( e 0.46317 3 )
but that is wrong on my assignment. What do I do with the 3 ? I tried multiplying it by the 8 to get 24 but that isn't right either.

Answer & Explanation

avuglantsaew

avuglantsaew

Beginner2022-11-12Added 15 answers

Note: ( 1.589 ) t 3 = ( 1.589 ) t ( 1.589 ) 3 . Then you have
y = 8 ( 1.589 ) 3 ( 1.589 ) t
Now, also notice that a = e ln ( a ) . Then this gives you
y = 8 ( 1.589 ) 3 e ln ( 1.589 t )
Since ln ( a t ) = t ln ( a ), then we arrive at
y = 8 ( 1.589 ) 3 e t ln ( 1.589 )
where a = ln ( 1.589 ) and A 0 = 8 ( 1.589 ) 3

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