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]

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

b) 975 people per square mile.

Step-by-step explanation:

(a)

The units of D(r) are  

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

(b)

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

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

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

answer

see attachment

explanation

the given function is

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.

x=30

step-by-step explanation: