After t weeks, a charity is raising money at the rate of 5,000 t ln(t + 1) dollars per week. How much money is raised during the first 10 weeks? Round to the nearest ten dollars.
A) $493,000
B) $493,480
C) $493,520
D) $493,550

Question

Quizplus · Accepted Answer

To find the total amount of money raised during the first 10 weeks, we need to integrate the given rate of money raised, $5,000t \ln(t + 1)$, with respect to $t$ from 0 to 10. The integral of $5,000t \ln(t + 1)$ gives us the total amount raised over the specified period. The integral of $5,000t \ln(t + 1)$ is not straightforward and typically requires techniques from calculus, specifically integration by parts or a numerical method. After performing the integration (or using a calculator/software that can handle symbolic integration), and evaluating it from 0 to 10, the result is approximately $493,480, which rounds to the nearest ten dollars as given in option B.

After T Weeks, a Charity Is Raising Money at the Rate