This seems extremely basic but I can't seem to wrap my head around the wording of this question - for some reason it's extremely confusing to me..


Suppose that D(r ) is a function which gives population density in hundreds of people per sq mile, within r miles of the center of a very small town. Assume that there are 100 people per sq mile within 5 miles of the town's center, and 350 people per square mile within 7 miles.
A. let T(r ) be the # 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 avg rate of change of the function T(r) over the interval [5,7]? Give answer with units
C. Approximate the value of t(6) using the answer to part B. do you suspect that this will under or overestimate and explain

Any help would be greatly appreciated

1. Just write T(r), put big parenthesis and write down 100 and 350 with r limits
2. dealing with a circular area, you'll be integrating rings. since the problem states r, most likely it'll be in polar.
you know the number of people from integrated area*density

hmm ... not too sure I follow what you're saying..

Does D(r) = c/r^2 + b or something? then solve for c and b using initial values or what..?

I'm sorry, haha
been too long, totally forgot what i said about polar. it's possible, but not intended.
I was thinking of something else.
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No, you're given d(r). they are simply
100 on r=0 to 5
350 on r=5 to 7

d(r) is a density function that relates the number of people per area.
T(r) is a function of population, which takes in count of 1.density and 2.area

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1. density is d(r)
2. Area of a circle is pi*r*r

T(r) = 100*pi*r*r on r=0 to 5
T(r) = T(5) + 350(pi*r*r-pi*5*5) on r=5 to 7

Thanks a lot man - much appreciated. As usual I overthought the question thinking we have to formulate an expression for D(r)