Activity 7.1.2.
Express the following statements as differential equations. In each case, you will need to introduce notation to describe the important quantities in the statement, so be sure to clearly state what your notation means.
(a)
The population of a town grows continuously at an annual rate of 1.25%.
(b)
A radioactive sample loses mass at a rate of 5.6% of its mass every day.
(c)
You have a bank account that continuously earns 4% interest every year. At the same time, you withdraw money continually from the account at the rate of $1000 per year.
(d)
A cup of hot chocolate is sitting in a 70\(^\circ\) room. The temperature of the hot chocolate cools continuously by 10% of the difference between the hot chocolate’s temperature and the room temperature every minute.
(e)
A can of cold soda is sitting in a 70\(^\circ\) room. The temperature of the soda warms continuously at the rate of 10% of the difference between the soda’s temperature and the room’s temperature every minute.
