Answer:
[tex]f(x) = \frac{108}{7} (\frac{7}{6})^x[/tex] or [tex]f(x) = 15.429(1.167)^x[/tex]
Step-by-step explanation:
No need for a calculator.
Assuming that the equation is in the form [tex]y = ab^x[/tex], 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 [tex]18 = ab^1, 21 = ab^2[/tex]. Now let's divide the equations to get rid of [tex]a[/tex]: [tex]\frac{21 = ab^2}{18 = ab^1} = \frac{21}{18} = \frac{7}{6} = b[/tex]. Now that we have [tex]b[/tex], we can plug in the value we just calculated to solve for [tex]a[/tex]: [tex]18 = a(\frac{7}{6} )^1[/tex], and solving for [tex]a[/tex], we get [tex]a = \frac{108}{7}[/tex].
So the [tex]f(x) = (\frac{108}{7})(\frac{7}{6} )^x[/tex]
This equation in decimal form (rounded to the nearest thousandth) is [tex]f(x) = 15.429(1.167)^x[/tex].
hope this helped! :)
