A certain country's GDP (total monetary value of all...

A certain country's GDP (total monetary value of all finished goods and services produced in that country) can be approximated by g(t) = 5,000 - 420e^{-0.07t} billion dollars per year (0 ? t ? 5), where t is time in years since January 2010. Find an expression for the total GDP G(t) of sold goods in this country from January 2010 to time t. HINT: [Use the shortcuts.] G(t) = Estimate, to the nearest billion dollars, the country's total GDP from January 2010 through June 2014. (The actual value was 20,851 billion dollars.) billion dollars.

Transcript

00:01 In this question it is given that the gdp that will represent by gt is equals to 5 ,000 minus 420, e -raised to the power negative 0 .070 billion dollar per year and we need to find the expression for the total gdp of the goods sold in a country from january 2010.

00:26 So that means we need to find the expression for the total gdp of the goods sold in a country from january 2010.

00:30 For the total gdp.

00:34 So to find the expression for the total gdp, we'll consider gt and we integrate it, that is integrating both the sides, that is 5 ,000 minus 420, e.

00:53 To the power negative 0 .07 dt, where the range is from 0 to t, t.

01:04 Now when we integrate this we will let this expression to be equals to capital gt which will helps in evaluating the expression for the total gdp.

01:15 Now on solving it we get 5 ,000 t minus 420 e raised to the power negative 0 .07 t then we have negative 0 .07 raised to the power negative 1 and it is from 0 to t now on solving it we get 5 ,000 t minus 420 divided by negative 0 .07 since i have written this term in the form of 1 divided by 0 .07 e raised to the power 0.

02:19 Negative 0 .070.

02:22 This will be the first term.

02:24 Then we have a negative sign.

02:26 Now on putting t is equal to 0, it will be 0.

02:29 Then we have a negative sign.

02:32 Then putting t is equal to 0, this term will become 1...

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