College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises: 109

Answer

$f(x)=\frac{1}{4}^x$

Work Step by Step

First, we have to find the function, by calculating the value of the base, $a$. If the function contains this point (-3,64), then $f(-3)=64$, This means: $a^{-3}=64$. By the law of exponents: $a^{-x}=(\frac{1}{a})^x$ Thus, the equation above is equivalent to: $(\frac{1}{a})^{3}=64$ We take the cube root of both sides: $\frac{1}{a}=4 \\a \cdot \frac{1}{a} = 4 \cdot a \\1=4a \\\frac{1}{4}=a$ Therefore, with $a=\frac{1}{4}$, the function is: $f(x)=(\frac{1}{4})^x$.
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