Question

1. Write the differential equation described in each situation. Label any variables you need, and specify the sign (positive or negative) of each constant.

2. (b) People immigrate to a country, causing its population to grow, at a constant rate. People emigrate, causing its population to shrink, at a rate proportional to the size of the population. (Assume no one is born and no one dies in this country. 4 points)

3. (c) A bottle of water sits in a cooler. Its temperature changes at a rate proportional to the difference between its temperature and the temperature of the cooler. The temperature of the cooler changes at a rate proportional to the difference between its temperature and the temperature of the water. It takes three times as much energy to change the temperature of the cooler as it does to change the temperature of the water, so that the constant of proportionality for the water is three times as large as the constant of proportionality for the cooler. (6 points)

Answer 1