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Mashutka [201]
4 years ago
11

Suppose that D(r) is a function which gives the population density, in hundreds of people per square mile, within r miles of the

center of a very small town. Assume that there are 100 people per square mile within 5 miles of the town’s center, and 350 people per square mile within 7 miles. a.Let T(r) be the number of people (in hundreds) who live within r miles of the city. Write an expression for T(r), in terms of r and D(r). b.What is the average rate of change of the function T (r) over the interval [5, 7]
Mathematics
1 answer:
borishaifa [10]4 years ago
5 0

Answer:

a) T(r) = r.D(r)

b) 975 people per square mile.

Step-by-step explanation:

(a)

The units of D(r) are  

\frac{hundreds\;of\;people}{mile^2}

when multiplying the density by the area we get the amount of people in that area, so

T(r)=rmile^2D(r)\frac{hundreds\;of\;people}{mile^2}=rD(r)\;hundreds\;of\;people

(b)

The average rate of change of T(r) over the interval [5,7] is

\frac{T(7)-T(5)}{7-5}=\frac{7D(7)-5D(5)}{2}

but D(7) = 350 and D(5) = 100, so

\frac{7D(7)-5D(5)}{2}=\frac{7*350-5*100}{2}=975

and the average rate of change of T(r) over the interval [5,7] is 975 people per square mile.

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