Question

The rate of recipt of income from the sales of vases from 1988 to 1993 can be approximated by R(t)= 100/(t+0.87)^2 billion dollars per year, where t is time in years since January 1988. Estimate to the nearest $1 billion, the total change in income from January 1988 to January 1993.

Answer choices are: $43, $53, $137, $98, $117

Answer 1

The correct option is 4.

Explanation:

It is given that the rate of recipt of income from the sales of vases from 1988 to 1993 can be approximated by

`R(t)=(100)/((t+0.87)^2)`

billion dollars per year, where t is time in years since January 1988.

We need to estimate the total change in income from January 1988 to January 1993.

`I=\int_(0)^(5)R(t)dt`

`I=\int_(0)^(5)(100)/((t+0.87)^2)dt`

`I=100\int_(0)^(5)(1)/((t+0.87)^2)dt`

On integration we get

`I=-100[(1)/((t+0.87))]_(0)^(5)`

`I=-100((1)/(5+0.87)-(1)/(0+0.87))`

`I=-100(-0.979)`

`I=97.9`

`I\approx 98`

The total change in income from January 1988 to January 1993 is $98. Therefore the correct option is 4.