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

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) (Show Source): You can put this solution on YOUR website!

At x = 0, f(x) = 2

Therefore,

At x=13, f(x) = 16

The value of must be real
i.e.

So the function is

Answer by greenestamps(13203) (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)

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