Find Exponential Equation from data points

[Ocasta]

Hi guys I'm helping my girlfriend with her Calc 1 homework and we seem to be stuck on this one problem. Am I missing something obvious?

Homework Statement

Homework Equations

$P = P_0 a^t$

$\frac{5}{20} = \frac{P_0 a^1}{P_0 a^{-1}}$

$\frac{1}{4} = a^2$

$a = \frac{1}{2}$

$5 = P_0 (1/2)^1$

$P_0 = 10$

$P(t) = 10 (1/2)^t$

 

[Ocasta]

... and a few seconds after I posted this, I realized that we're using the wrong variable. X instead of t, and it works.

Rage! Rage factorial