Question

solve.

1. the total number of dollars donated each year to a small charitable organization has followed the trend ( d(t) = 2t^3 + 10t^2 + 2000t + 10000 ), where ( d ) is dollars and ( t ) is the number of years since 1990. the total number of donors each year has followed the trend ( p(t) = t^2 + 1000 ). write an expression describing the average number of dollars per donor.

Explanation:

Step1: Recall the formula for average

The average number of dollars per donor is the total dollars donated divided by the total number of donors. So we need to divide \( d(t) \) by \( p(t) \).

Step2: Substitute the given functions

We know \( d(t)=2t^{3}+10t^{2}+2000t + 10000 \) and \( p(t)=t^{2}+1000 \). So the average \( A(t) \) is \( \frac{d(t)}{p(t)}=\frac{2t^{3}+10t^{2}+2000t + 10000}{t^{2}+1000} \).

Answer:

\(\frac{2t^{3}+10t^{2}+2000t + 10000}{t^{2}+1000}\)