Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.7 Write and Apply Exponential and Power Functions - 7.7 Exercises - Skill Practice - Page 533: 13


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Work Step by Step

Given: $(1,9.8);(2,12.2);(3,15.2);(4,19);(5,23.8)$ Find some values: $x=1 \rightarrow \ln y=2.28\\ x=2 \rightarrow \ln y=2.5\\x=3 \rightarrow \ln y=2,72\\x=4 \rightarrow \ln y=2.94\\x=5 \rightarrow \ln y=3.17$ Take two points $(1,2.28;5,3.17)$ Find the slope of the line passing through those two points: $m=\frac{3.17-2.28}{5-1}=\frac{0.89}{4}=0.2225$ Thus, $\ln y-2.28=0.2225(x-1)\\\ln y-2.28=0.2225x-0.2225\\\ln y=0.2225x+2.0575\\y=e^{0.2225x+2.0575}\\y=e^{0.2225x}(e^{2.0575})\\y=7.83(1.25)^x$
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