Question

1. Calculate the population within a 7-mile radius of the city center if the radial population density is
ρ(r) = 5(5 + r2)1/3
(in thousands per square mile). (Round your answer to two decimal places.)

2. A population of insects increases at a rate
280 + 8t + 1.5t2
insects per day. Find the insect population after 5 days, assuming that there are 40 insects at
t = 0.
(Round your answer to the nearest insect.)

Answer 1

consider the population as a collection of rings of thickness dr. Each ring's population is the area of the ring times its density. Add them all up and you get

p(r) = ∫[0,7] 2πr*5(5+r^2)^(1/3) dr

for the insects,

dp/dt = 280 + 8t + 1.5 t^2
p(t) = 40 + 280t + 4t^2 + 3t^3

Answer 2

p(t) = 40 + 280t + 4t^2 + 3t^3
I think it is
p(t) = 40 + 280t + 4t^2 + (1/2)t^3

Answer 3

oh yeah - Good catch