Question

How do I solve this question?

Answer 1

`f(x) = (108)/(7) ((7)/(6))^x` or
`f(x) = 15.429(1.167)^x`

Explanation:

No need for a calculator.

Assuming that the equation is in the form
`y = ab^x`, we can plug in points to get our equation. For ease, let's use (1,18) and (2,21). When plugging these points in, we get
`18 = ab^1, 21 = ab^2`. Now let's divide the equations to get rid of
`a`:
`(21 = ab^2)/(18 = ab^1) = (21)/(18) = (7)/(6) = b`. Now that we have
`b`, we can plug in the value we just calculated to solve for
`a`:
`18 = a((7)/(6) )^1`, and solving for
`a`, we get
`a = (108)/(7)`.

So the
`f(x) = ((108)/(7))((7)/(6) )^x`

This equation in decimal form (rounded to the nearest thousandth) is
`f(x) = 15.429(1.167)^x`.

hope this helped! :)