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.

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

To find the rate at which people relocated during the year of your birth, you need to evaluate the derivative of the given function at that particular time.

1. The function that represents the population relocation percentage is p(t) = 20.6e^(-0.009t).

To find the rate, you need to take the derivative of this function with respect to time (t). The derivative of e^(-0.009t) is -0.009e^(-0.009t) using the chain rule. Therefore, the rate at which people relocated at any given time t is given by:

p'(t) = -0.009 * 20.6e^(-0.009t)

To find the rate during the year of your birth, substitute the appropriate value of t. If your birth year is y, then t would be y - 1960 (since t = 0 corresponds to 1960).

2. To find the current relocation rate, substitute the value of t as the current year minus 1960.

Now let's address the other questions:

What does this tell you about the country’s population?
The given function, p(t), gives the percentage of the population relocating at any given time t. By calculating the rate of relocation, we can assess the rate at which people are moving. This provides insight into population movement trends.

Is there a peak (max) relocation year?
To find the peak relocation year, we need to find the year where the relocation rate is highest. To determine this, we can find the maximum value of the rate function, p'(t), by calculating its derivative, setting it equal to zero, and solving for t. This will give us the year with the maximum relocation rate.

Do you think this model is appropriate for predicting population movement?
To determine if this model is appropriate for predicting population movement, we need to assess its accuracy by comparing its predictions with actual data. Additionally, we can compare our calculations and insights with classmates to identify any discrepancies or similarities in our conclusions. By engaging in this comparison, we can collectively evaluate the model's effectiveness.