Question

find the exponential function f(x)=ab^x, if f(0) = 64, and f(2)=4

Answer 1

f(0) = 64.
At zero,
function is like a . b ^0
We know that anything to the power 0 = 1
therefore we get a = 64.

Now at 2,
function is like,
a . b ^ 2 = 4
a is 64.
Therefore,
b ^2 = 1/16 = 4 ^ (-2)
Comparing it gives us b = 4.
There fore function is,
64 . 4^x