Algebra 2 Common Core

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

Chapter 7 - Exponential and Logarithmic Functions - 7-1 Exploring Exponential Models - Lesson Check: 4

Answer

This graph represents exponential decay The y-intercept of this graph is (0, 1)

Work Step by Step

In order to determine whether this graph represents exponential growth or exponential decay, we must first remember that exponential growth and decay functions look like this: ${y}$ = ${a}$${b}$$^{x}$ ${a}$ = y-intercept ${b}$ = Rate of growth/decay If ${b}$ is between 0 up to but not including 1, the function is exponential decay. If ${b}$ is greater than 1, the function is exponential growth. In the case of this question, ${b}$ is equal to 0.95, which is less than one but greater than zero. Therefore, this function is an exponential decay function. To find the y-intercept, look at ${a}$. In this case, there does not appear to be an ${a}$, so it must be equal to 1. This function intersects the y-axis at 1 units up, or (0, 1)
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