1. In a certain country, the percentage of the population relocating to a new town is given by the following function:


p(t) = 20.6e^-0,009t,where 0 _< t _< 52.

Time is zero (t = 0) corresponds to the year 1960.

1. Find the rate at which people relocated during the year of your birth. Which is 1981

2. Find the relocation rate of today.

What does this tell you about the country’s population? Is there a peak (max) relocation year? Do you think this model is appropriate for predicting population movement? Share and compare calculations with another classmate

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To find the rate at which people relocated during the year of your birth (1981), we need to calculate the derivative of the given function p(t) with respect to time (t), and then substitute t = 21 (since 1981 corresponds to t = 21).

1. Calculate the derivative of p(t):
p'(t) = (-0.009) * 20.6 * e^(-0.009t)

2. Substitute t = 21 into the derivative:
p'(21) = (-0.009) * 20.6 * e^(-0.009(21))

Now, you can use a calculator or software to evaluate the expression for p'(21). This will give you the relocation rate during the year of your birth.

To find the current relocation rate, we need to substitute t = 2021 - 1960 = 61 (assuming the current year is 2021).

3. Substitute t = 61 into the original function p(t):
p(61) = 20.6 * e^(-0.009(61))

Again, you can use a calculator or software to evaluate the expression for p(61). This will give you the current relocation rate.

Comparing the relocation rates for the year of your birth and the current year will provide insights into the country’s population movement. If the rate has significantly changed over the years, it suggests that the population relocation patterns have undergone a shift.

To determine if there is a peak (max) relocation year, you can analyze the function p(t) to find the highest value it takes within the given time interval (0 ≤ t ≤ 52). You can do this by finding the maximum of p(t) or analyzing its derivative to locate critical points.

Regarding the appropriateness of this model for predicting population movement, it is difficult to make a conclusive judgment without additional information or comparing the model's predictions with real historical data. It may be helpful to discuss and compare your calculations and observations with a classmate to gain different perspectives.