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
1. To find the rate at which people relocated during the year of your birth, you need to calculate the derivative of the given function p(t) with respect to time (t). The derivative will give you the rate of change of population relocation.
The derivative of p(t) = 20.6e^(-0.009t) with respect to t can be found using the chain rule of differentiation. The derivative is given by:
p'(t) = -0.009 * 20.6e^(-0.009t)
To find the rate at which people relocated during the year of your birth, substitute the value of t corresponding to the year of your birth into p'(t) and calculate the result.
2. To find the relocation rate of today, substitute the current value of t (52, since the function is defined for t from 0 to 52) into p'(t) and calculate the result.
The relocation rate calculated in 1 and 2 will provide information about the rate at which people relocated during your birth year and the present day, respectively.
To determine if there is a peak (maximum) relocation year, you can plot the function p(t) over the given time range (0 to 52) and observe any local maxima. If there is a year where the relocation rate reaches its highest value, that year would be the peak relocation year.
Regarding whether this model is appropriate for predicting population movement, you can compare your calculations with another classmate who has also used the same model. If both your calculations and your classmate's calculations provide reasonably accurate results in comparison with available data or other models, then this model may be considered appropriate for predicting population movement in the given country.