Algebra 2 Common Core

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

Chapter 7 - Exponential and Logarithmic Functions - 7-2 Properties of Exponential Functions - Practice and Problem-Solving Exercises - Page 450: 52

Answer

$\text{exponential decay}$; $y$-intercept = $2$

Work Step by Step

RECALL: The exponential function $y=c \cdot b^x$ represents: (1) an exponential growth when $b\gt 1$. (2) an exponential decay when $0\lt b \lt 1$. The given exponential function has $b=\frac{3}{4}$, which is less than $1$. Thus, the exponential function represents an exponential decay. The $y$-intercept can be found by setting $x=0$ then solving for $y$: \begin{align*} y&=2\left(\frac{3}{4}\right)^x\\ y&=2\left(\frac{3}{4}\right)^0\\ y&=2(1)\\ y&=2 \end{align*} Therefore, the $y$-intercept is $2$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.