Checkpoint: Writing Exponential Equations Solution

Write an exponential equation that passes through the points $(- 1, 0.6)$ and $(2, 75) .$

$\begin{array}{rcl} \begin{matrix} y = a b^{x} \\ 0.6 = a b^{- 1} & 75 = (0.6 b) b^{2} \\ 0.6 = \frac{a}{b} & \frac{75}{0.6} = \frac{0.6 b^{3}}{0.6} & a = 0.6 (5) \\ a = 0.6 b & \sqrt[3]{125} = \sqrt[3]{b^{3}} & a = 3 \\ b = 5 & y = 3 {(5)}^{x} \end{matrix} \end{array}$

Note

Remember, when you multiply bases, you add exponents.

Q: Does the exponential function represent growth or decay? Explain.

A: This is a growth equation because $b > 1 .$