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: 1

Answer

The function represents exponential decay and the y-intercept is at $(0,10).$

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 this case, $b = 0.45$, which is less than $1$, which means that the function represents exponential decay. To find the Y-intercept, we plug in $0$ for $x$. $y = 10(0.45)^0 = 10(1) = 10$ The y-intercept is $(0,10)$.
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