SOLUTION: An exponential function of the form passes through the points (2,15) and (4, 15/4) . Find an equation of f(x).

Algebra ->  Functions -> SOLUTION: An exponential function of the form passes through the points (2,15) and (4, 15/4) . Find an equation of f(x).       Log On


   

Question 1180950: An exponential function of the form passes through the points (2,15) and (4, 15/4) . Find an equation of f(x).
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52752) About Me  (Show Source):
You can put this solution on YOUR website!
.

Due to your inaccuracy, the form of the exponential function is missed in your post.


Without this information, the problem can not be solved: it has INFINITELY MANY solutions,
from which it is IMPOSSIBLE to select a UNIQUE SOLUTION.


The missed info is vitally important for the solution.



Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


I will assume the form you want is the standard exponential: f%28x%29=a%28b%5Ex%29

Get two equations that can be solved for a and b using the two given points.

15=ab%5E2
15%2F4=ab%5E4

Divide one equation by the other to eliminate a and solve for b.

4+=+b%5E%28-2%29
b%5E2=1%2F4
b=1%2F2

Use that value of b to solve for a.

15=ab%5E2=a%281%2F4%29
a=60

ANSWER: f%28x%29+=+60%28%281%2F2%29%5Ex%29