Question 1161510: The population of a town is modelled by P(t) = -t^2 + 12t + 4, where P(t) is the number of years since 2000. What is the average rate of change in population on size from 2005 to 2010?
a) 3000 people/year
b) 6000 people/year
c) 10 000 people/year
d) 15 000 people/year
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
The year 2005 is 5 years after the year 2000
Plug in t = 5 to find the population in 2005
P(t) = -t^2 + 12t + 4
P(5) = -(5)^2 + 12(5) + 4
P(5) = -25 + 60 + 4
P(5) = 35 + 4
P(5) = 39
The population in 2005 is 39,000 (assuming P(t) measures the population in thousands of people)
Repeat for t = 10 to get the population in 2010
P(t) = -t^2 + 12t + 4
P(10) = -10^2 + 12(10) + 4
P(10) = -100 + 120 + 4
P(10) = 20 + 4
P(10) = 24
The population is now 24,000
The change in population is 39,000-24,000 = 15,000
So the population has dropped 15,000 people
This is over a span of 5 years, so the rate is 15,000/5 = 3,000 people per year.
In other words, 3000 people are leaving this town each year.
I would argue it would be better to use a negative number to indicate population decline (and say the rate of change is -3000 people/year); however, your teacher has gone with positive numbers only for the answer choices. Without further context, those answer choices imply population growth.
Answer: choice A) 3000 people/year are leaving the town.
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