SOLUTION: Find A and k if the general equation is y=Ae^kx given two points (-2,-10) and (-1,-4). correct to two decimal places.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find A and k if the general equation is y=Ae^kx given two points (-2,-10) and (-1,-4). correct to two decimal places.      Log On


   

Question 287740: Find A and k if the general equation is y=Ae^kx given two points (-2,-10) and (-1,-4). correct to two decimal places.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+A%2Ae%5E%28kx%29
(-2,-10)
(1) -10+=+A%2Ae%5E%28k%2A%28-2%29%29
(-1,-4)
(2) -4+=+A%2Ae%5E%28k%2A%28-1%29%29
Solve both equations for A
(1) A+=+-10%2Ae%5E%282k%29
(2) A+=+-4%2Ae%5Ek
so,
-10%2Ae%5E%282k%29+=+-4%2Ae%5Ek
e%5E%282k%29%2Fe%5Ek+=+2%2F5
%28e%5Ek%29%5E2%2Fe%5Ek+=+2%2F5
e%5Ek+=+2%2F5
k+=+ln%28.4%29
k+=+-.92
and
(2) A+=+-4%2Ae%5Ek
A+=+-4%2Ae%5E%28-.92%29
A+=+-4%2A.4
A+=+-1.6