# How do you estimate the instantaneous rate of change in population in 2010 if a city's population (tens of thousands) is modeled by the function #p(t) = 1.2(1.05)^t# where t is number of years since 2000?

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To estimate the instantaneous rate of change in population in 2010, you can find the derivative of the population function with respect to time, and then evaluate it at t = 10 (since 2010 is 10 years after 2000).

First, find the derivative of the population function, p(t), with respect to t:

p'(t) = 1.2 * ln(1.05) * (1.05)^t

Then, evaluate the derivative at t = 10:

p'(10) = 1.2 * ln(1.05) * (1.05)^10

You can then calculate the numerical value of p'(10) to estimate the instantaneous rate of change in population in 2010.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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