The rate of depreciation of a building is given by $D ^ { \prime } ( t ) = 8,300 ( 20 - t )$ dollars per year, $0 \leq t \leq 20$ Use the definite integral to find the total depreciation over the first $20$ years.
A) $\$ 1,660,000$
B) $\$ 83,000$
C) $\$ 830,000$
D) $\$ 474,286$
E) $\$ 3,320,000$

Question

Quizplus · Accepted Answer

The total depreciation over the first 20 years can be found by integrating the rate of depreciation from $t = 0$ to $t = 20$. The integral is $\int_{0}^{20} 8300(20 - t) dt$, which simplifies to $8300 \times \left[20t - \frac{1}{2}t^2\right]_{0}^{20}$. Evaluating this gives $8300 \times (400 - 200) = 8300 \times 200 = 1,660,000$.

The Rate of Depreciation of a Building Is Given By D