Algebra 2 Common Core

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

Chapter 7 - Exponential and Logarithmic Functions - Chapter Test - Page 491: 3

Answer

$\text{exponential growth}$; $y$-intercept = $0.1$

Work Step by Step

RECALL: The exponential function $y=c \cdot a^x$ represents an exponential: (i) decay when $0\lt a \lt 1$; (ii) growth when $a \gt 1$ The given exponential function has $a=10$ which is greater than $1$. Thus, the given function represents exponential growth. The $y$-intercept of a function can be found by sestting $x=0$ then solving for $y$. Hence, the $y$-intercept is \begin{align*} y&=0.1 \cdot \left(10\right)^{x}\\ y&=0.1 \cdot 10^0\\ y&=0.1 (1)\\ y&=0.1 \end{align*}
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