Question

How do you find the exponential function formula for the points g(2)=45 and g(4)=405?

Answer 1

An exponential function is generally of the form `y = ac^x`

Explanation:

`y = ac^x`

Writing a system of equations to solve for `a and c`

`45 = ac^2`

`405 = ac^4`

`405/c^4 = a`

`45 = 405/c^4(c^2)`

`45 = 405/c^2`

`45c^2 = 405`

`c^2 = 9`

`c = 3`

`45 = a(3^2)`

`45 = 9a`

5 = a#

Therefore, your equation is `y = 5 xx 3^x`