Based on census data, the population of Freedonia is modeled by the function P(t)=265t^2+36600 people, where t represents the number of years after 1990. Use this function to determine in which year the population of Freedonia was increasing at a rate of 2650 people per year.
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This is the second time you have reposted after the original has
been answered.
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I have had a hard time looking for the questions I posted, so I keep posting it again to give me similar questions? Is there any way to see the questions I have posted?
It's only 3 and 6 posts down from here.
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To determine the year when the population of Freedonia was increasing at a rate of 2650 people per year, we need to find the derivative of the population function P(t) and then set it equal to 2650.
The derivative of the population function with respect to time, P'(t), gives us the rate at which the population is changing. We can find the derivative of P(t) by differentiating each term of the function.
P(t) = 265t^2 + 36600
Differentiating, we get:
P'(t) = 2 * 265t + 0
Simplifying:
P'(t) = 530t
Now we can set P'(t) equal to the given rate of increase, 2650, and solve for t:
530t = 2650
Dividing both sides by 530:
t = 2650 / 530
Simplifying:
t = 5
So, t representing the number of years after 1990 is 5. Therefore, to determine the year when the population of Freedonia was increasing at a rate of 2650 people per year, we add 5 to 1990:
Year = 1990 + 5 = 1995
Thus, the population of Freedonia was increasing at a rate of 2650 people per year in the year 1995.