A major corporation is building a 4,325-acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Cove's population (in thousands) t years from now will be given by (25t2 + 150t + 100)/(t2 + 6t + 24)
A) Find the rate at which Glen Cove's population is changing with respect to time.
B) What will be the population after 10 years?
C) At what rate will the population be increasing when t = 10?

See explanation

Step-by-step explanation:

We have that;

P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)

a) rate at which Glen Cove's population is changing with respect to time.

dP/dt = (t^2 + 5t + 40) (50t + 125) - (25t^2 + 125t + 200) (2t + 5)/(t^2 + 5t + 40)^2

dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2

b)  population after 10 years

P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)

P(t) =(25(10)^2 + 150(10) + 100)/((10^2 + 6(10) + 24)

P(t) = 4100/184

P(t) = 22283

c) when t = 10

dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2

dP/dt = 1000(10) + 3000/(10^2 + 6(10) + 24)^2

dP/dt = 13000/33856

dP/dt = 0.384

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.