Chapter 7 Exponential and Logarithmic Functions - 7.7 Write and Apply Exponential and Power Functions - 7.7 Exercises - Skill Practice - Page 533: 12

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Given: $(1,3.3);(2,10.1);(3,30.6);(4,92.7);(5,280.9)$ Find some values: $x=1 \rightarrow \ln y=1.19\\ x=2 \rightarrow \ln y=2.31\\x=3 \rightarrow \ln y=3.421\\x=4 \rightarrow \ln y=4.53\\x=5 \rightarrow \ln y=5.64$ Take two points $(1,1.19;5.64)$ Find the slope of the line passing through those two points: $m=\frac{5.64-1.19}{5-1}=\frac{4.44}{4}=1.11$ Thus, $\ln y-1.19=1.11(x-1)\\\ln y-1.19=1.11x-1.11\\\ln y=1.11x+0.08\\y=e^{1.11x+0.08}\\y=e^{0.08}(e^{1.11x})\\y=1.08(3.03)^x$