Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 364: 106

Answer

$$y=600(1.05)^t$$

Work Step by Step

Note that $\frac{630}{600} = \frac{661.5}{630} = \frac{694.58}{661.5} = \frac{729.3}{694.58} = 1.05$ So, each next number is 1.05 times the previous number. $$y(t+1) = 1.05y(t)$$ We are given that it is an exponential function so $$y(t)=Cb^t$$ By this, we get, $Cb^{t+1}= 0.6Cb^t$ Or $$b=1.05$$ Putting t = 0 gives, $y(0) = Cb^0 =600$ Or $$C = 600$$ Therefore, $$\boxed{y=600(1.05)^t}$$
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