Question

How do I solve this question?

Answer 1

Answer:

$f(x) = \frac{108}{7} (\frac{7}{6})^x$ or $f(x) = 15.429(1.167)^x$

Step-by-step 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 $a$: $\frac{21 = ab^2}{18 = ab^1} = \frac{21}{18} = \frac{7}{6} = b$. Now that we have $b$, we can plug in the value we just calculated to solve for $a$: $18 = a(\frac{7}{6} )^1$, and solving for $a$, we get $a = \frac{108}{7}$.

So the $f(x) = (\frac{108}{7})(\frac{7}{6} )^x$

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

hope this helped! :)