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: 14


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Work Step by Step

Given: $(1,1.4);(2,6.7);(3,32.9);(4,161.4);(5,790.9)$ Find some values: $x=1 \rightarrow \ln y=0.336\\ x=2 \rightarrow \ln y=1.9\\x=3 \rightarrow \ln y=3.49\\x=4 \rightarrow \ln y=5.08\\x=5 \rightarrow \ln y=6.673$ Take two points $(1,0.336;5,6.673)$ Find the slope of the line passing through those two points: $m=\frac{6.673-0.336}{5-1}=\frac{6.337}{4}=1.584$ Thus, $\ln y-0.336=1.584(x-1)\\\ln y-0.336=1.584x-1.584\\\ln y=1.584x-1.248\\y=e^{1.584x-1.248}\\y=e^{-1.248x}(e^{1.584})^x\\y=0.287(4.87)^x$
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