SOLUTION: Find the exponential function f(x)=Ca^x whose graph goes through the points (0,2)and (3,16).

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the exponential function f(x)=Ca^x whose graph goes through the points (0,2)and (3,16).      Log On


   

Question 1148543: Find the exponential function
f(x)=Ca^x
whose graph goes through the points
(0,2)and (3,16).
Found 2 solutions by psbhowmick, greenestamps:
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+C%2Aa%5Ex
At x = 0, f(x) = 2
2+=+C%2Aa%5E0
2+=+C%2A1
C+=+2

Therefore, f%28x%29+=+2%2Aa%5Ex

At x=13, f(x) = 16
16+=+2%2Aa%5E3
a%5E3+-+8+=+0
%28a+-+2%29%28a%5E2+%2B+2a+%2B+4%29=0

The value of a must be real
a+-+2+=+0 i.e. a+=+2

So the function is
f%28x%29+=+2%2A2%5Ex

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Using the two given points in the general form of the equation....

(1) 2 = Ca^0 = C*1 = C; so C=2. Then

(2) 16 = Ca^3 = 2a^3; so a^3 = 8; a = 2.

ANSWER: C=2; a=2; f(x) = 2(2^x)