Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - Mid-Chapter Quiz - Page 461: 3


$\text{exponential growth;}$ $y$-intercept = $\dfrac{7}{8}$

Work Step by Step

Recall: The exponential function $y=c \cdot b^x$ involves exponential: (i) growth when $b\gt 1$ (ii) decay when $0 \lt b \lt 1$ The given exponential function has $b=18$, which is greater than $1$, therefore it involves exponential growth. The $y$-intercept of a function can be found by setting $x=0$ then solving for $y$. Set $x=0$ then solve for $y$ to obtain: \begin{align*} y&=\frac{7}{8}\left(18\right)^x\\\\ y&=\frac{7}{8}\left(18\right)^0\\\\ y&=\frac{7}{8}(1)\\\\ y&=\frac{7}{8} \end{align*} Thus, the $y$-intercept is $\dfrac{7}{8}$.
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