Algebra 2 Common Core

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

Chapter 7 - Exponential and Logarithmic Functions - 7-6 Natural Logarithms - Practice and Problem-Solving Exercises - Page 483: 82



Work Step by Step

Recall: If $y$ varies directly as $x$, then $y=kx$ where $k$=constant of variation. When $x=2$, the value of $y$ is $4$. Substitute these values into the equation above to obtain: \begin{align*} y&=kx\\\\ 4&=k(2)\\\\ 4&=2k\\\\ \frac{4}{2}&=\frac{2k}{2}\\\\ 2&=k \end{align*} Thus, the direct variation is $y=2x$. To find $y$ when $x=5$, substitute $5$ to $x$ to obtain: \begin{align*} y&=2x\\ y&=2(5)\\ y&=10 \end{align*}
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