Generate an image of a small town viewed from a hilltop, showing an assortment of well-spaced buildings such as houses, a school, a grocery store, and a few essential services. In the foreground, depict a grid of paper hosting a functional graph, showing a curve that represents a mathematical function. Superimpose this grid subtly against the background, symbolizing the connection between the town's population and the function. The town should appear tranquil and welcoming amidst a lush green setting, with a river slowly flowing by its side. The sky is clear with a few fluffy, white clouds.

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.

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.

@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

I got 12 not 12,000 for the first one

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

chicken cheese curds

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

@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.