Question

Find the equation of the exponential function represented by the table below:

Answer 1

`y =5(3)^x`

Explanation:

Given

The attached table

Required

Determine the equation of the table

The table represents an exponential function. So, we make use of

`y = ab^x`

When x = 0, y= 5.

So:

`y = ab^x` becomes

`5 = ab^0`

`5 = a*1`

`5 = a`

`a = 5`

When x = 1; y = 15

So;

`y = ab^x` becomes

`15 = a * b^1`

`15 = a * b`

Substitute 5 for a

`15 = 5 * b`

Divide both sides by 5

`(15)/(5) = (5 * b)/(5)`

`3 = b`

`b = 3`

Substitute values for a and b in:
`y = ab^x`

`y =5(3)^x`