MAT $213$ Brief Calculus

$14\mathrm{.}2$ Area between two curves

Name: $q,$

The following models provide the rates of change of the number of game apps in Apple's App Store and Google's Play Store for the period $2010-2020.$

Apple: $a(t)=-8t^{2}90t-98$ thousand apps per year on $0t10$

Google: : $g(t)=-7t^{2}52t7$ thousand apps per year on $0t10$ where $t$ is time in years since the middle of $2010.$

A$)[10$ pts$]$ Estimate and interpret the area from mid$-2010$ to mid$-2013.$ Include units

B$)[10$ pts$]$ Estimate and interpret the area from mid$-2013$ to mid$-2020.$ Include units and round to the nearest thousand

C$)[5$ pts$]$ Graph the two functions and represent your answers in A and B$.$ Clearly label your graph

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Task

The following models provide the rates of change of the number of game apps in Apple's App Store and Google's Play Store for the period $2010-2020.$

Apple: $a(t)=-8t^2+90t-98$ thousand apps per year on $0t10$

Google: $g(t)=-7t^2+52t+7$ thousand apps per year on $0t10$

where $t$ is time in years since the middle of $2010.$

A$)[10$ pts$]$ Estimate and interpret the area from mid$-2010$ to mid$-2013.$ Include units

B$)[10$ pts$]$ Estimate and interpret the area from mid$-2013$ to mid$-2020.$ Include units and round to the nearest thousand

C$)[5$ pts$]$ Graph the two functions and represent your answers in A and B$.$ Clearly label your graph