Question #dc81f

1 Answer
Radioactive Teddybear
Nov 22, 2017

5(1/(2e^2)+7) or ~35.33834

Explanation:

let's make the exponential decay graph f(x) graph{e^(-0.4x) [-7.024, 7.024, -3.51, 3.514]}
and the linear graph g(x)
graph{2.4x+1 [-7.024, 7.024, -3.51, 3.514]}

Judging by the graphs, the linear graph will be the "upper curve" from 0 to 5 since it is greater than the exponential decay graph at all points (0,5]

So it will be integration of upper area minus lower area for the domain, or int_0^5g(x)-f(x)dx.
Then you substitute the equations, so
int_0^5(2.4x+1)-(e^(-0.4x))dx
=int_0^5 2.4x+1-e^(-0.4x)dx

Then you can integrate and solve using the 2nd Fundamental Theorem of Calculus.

int_0^5 2.4x+1-e^(-0.4x)dx
=(1.2x^2+x+2.5e^(-0.4x))|_0^5
=1.2*5^2+5+2.5e^(-0.4*5)-(0)
=5(1/(2e^2)+7) or ~35.33834

Ask if you need any clarification on this. Thanks for asking though.

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