# MATH

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.

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.

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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.

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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.

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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

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

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5. I got 12 not 12,000 for the first one

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

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