If r(t)represents the rate at which a country's debt is growing, then the increase in its debt between 1990 and 2000 is given by
A) $\frac{r(2000)-r(1990)}{2000-1990}$
B) $r(2000)-r(1990)$
C) $\frac{1}{10} \int_{1990}^{2000} r(t) d t$
D) $\int_{1990}^{2000} r(t) d t$
E) $\frac{1}{10} \int_{1990}^{2000} r^{\prime}(t) d t$

Question

Quizplus · Accepted Answer

The increase in the country's debt over a period is calculated by integrating the rate of change of the debt (r(t)) over that period. Therefore, the integral from 1990 to 2000 of r(t) dt gives the total increase in debt over those years.

If R(t)represents the Rate at Which a Country's Debt Is r(2000)−r(1990)2000−1990\frac{r(2000)-r(1990)}{2000-1990}2000−1990r(2000)−r(1990)​

If R(t)represents the Rate at Which a Country's Debt Is $\frac{r(2000)-r(1990)}{2000-1990}$