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

Answer:

The correct option is 4.

Step-by-step explanation:

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

$R(t)=\frac{100}{(t+0.87)^2}$

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.

$I=\int_{0}^{5}R(t)dt$

$I=\int_{0}^{5}\frac{100}{(t+0.87)^2}dt$

$I=100\int_{0}^{5}\frac{1}{(t+0.87)^2}dt$

On integration we get

$I=-100[\frac{1}{(t+0.87)}]_{0}^{5}$

$I=-100(\frac{1}{5+0.87}-\frac{1}{0+0.87})$

$I=-100(-0.979)$

$I=97.9$

$I\approx 98$

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