Question

Write an exponential function in the form y=ab^xy=ab

x
that goes through points (0, 18)(0,18) and (2, 288)(2,288).

Answer 1

`y = 18*4^x`

Explanation:

We want an exponential equation in the following format:

`y = ab^x`

Point (0,18):

This means that when
`x = 0, y = 0`. So

`y = ab^x`

`18 = ab^0`

`a = 18`

So

`y = 18b^x`

Point (2,288):

This means that when
`x = 2, y = 288`. So

`y = 18b^x`

`18b^2 = 288`

`b^2 = (288)/(18)`

`b^2 = 16`

`b = 4`.

So

`y = 18*4^x`