Question

4. The population of a small town is modelled by the function
p(t)= 20(4t+3)/2t+5
, where P(t) is the population, in thousands, and t is time, in years, since the start of 1990.
a) Is the population currently increasing or decreasing? Justify your answer.

b) The town will need its own transit system if the population exceeds
50 000. Will the town’s population ever exceed 50 000? Explain.

Answer 1

P(t) = 20(4t+3)/(2t+5)
a. Population in 1990: Let t =0. Solve
for P and get 12,000.

Population in 2000: Let t = 10.
P = 34,400.

Population in 2010: Let t = 20.
P=36,889. Therefore the population is
growing.

b. Replace P with 50 and solve for t.
You should get -9.5 years. The time
cannot be negative. Therefore, the
population cannot reach 50,000.

Answer 2

@Henry There's no way you get -9.5 years for part b, so I'm not sure what drugs you were on when you came up with that solution.

Answer 3

@Fermoblazer101 you are wrong for part b you will get -9.5

b)Replace P with 50 and solve for t.
50=20(4t+3)/2t+5
50(2t+5)=20(4t+3)
100t+250=80t+60
100t-80t=60-250
20t=-190
t=-190/20
t=-9.5

Answer 4

Sorry How did you get 12,000 for the first part?

Answer 5

I got 12 not 12,000 for the first one

Answer 6

and for part b why do you replace p for 50? thanks

Answer 7

chicken cheese curds