Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 20)(0,20) and (2, 720)(2,720).

Answer 1

The exponential function that goes through
`(x_(1),y_(1)) = (0,20)` and
`(x_(2), y_(2)) = (2,720)` is
`y = 20\cdot 6^(x)`.

Explanation:

Let be an exponential function of the form
`y = a\cdot b^(x)` that goes through
`(x_(1),y_(1)) = (0,20)` and
`(x_(2), y_(2)) = (2,720)`. Then, we have the following system of equations:

`20 = a\cdot b^(0)` (1)

`720 = a\cdot b^(2)` (2)

By dividing (2) by (1), we obtain the value for
`b`:

`(720)/(20) = b^(2)`

`b = \sqrt{(720)/(20) }`

`b = 6`

And the value for
`a` is found by (1):

`a = 20`

The exponential function that goes through
`(x_(1),y_(1)) = (0,20)` and
`(x_(2), y_(2)) = (2,720)` is
`y = 20\cdot 6^(x)`.