Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.3 Exponential Functions - 5.3 Assess Your Understanding - Page 281: 29


exponential; $H(x)=$4^x$

Work Step by Step

The ratio of consecutive values is constant (because $\dfrac{1}{\frac{1}{4}}=\frac{4}{1}=\frac{16}{4}=\frac{64}{16}=4$), hence, the function is exponential with a common ratio of $4$. The difference of consecutive values is not constant ($4-1=3\ne16-4=12$) hence, the function is not linear. A function that models the data: (with a common ratio of $4$ and $H(0)=1$) is $H(x)=4^x$.
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