College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.2 - Page 468: 132

Answer

$t = 9$ months

Work Step by Step

$$f(t) = 75 - 10\log(t+1)$$ To find the value of $t$ where the average score falls below 65, we can do the following: $$f(t) = 65 = 75-10\log(t+1)$$ $$-10 = -10\log(t+1)$$ $$1 = log_{10}(t+1)$$ $$10^1 = t+1$$ $$10-1 = 9 = t$$ By looking at the graph and drawing a line at $y=65$, we confirm this by noticing that the graph crosses it at around $x =9$, which is to say, $9$ months.
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