9514 1404 393
Answer:
f(x) = 4·3^x
Explanation:
We assume the function will be of the form ...
f(x) = a·b^x
Substituting the given values, we can find 'a' and 'b'.
4/9 = a·b^(-2)
108 = a·b^3
Dividing the second equation by the first gives ...
108/(4/9) = b^(3 -(-2))
243 = b^5
b = 3 . . . . . . 5th root
Using the second equation, we can find 'a':
108 = a·3^3 = 27a
a = 108/27 = 4
The formula for the exponential function is ...
f(x) = 4·3^x