Chapter 9.C, Problem 30E

. Exponential growth and decay laws. Consider the following cases of exponential growth and decay.

1. Create an exponential function of the form \[Q = {Q_0} \times {(1 + r)^t}\] (where r >0 for growth and r <0 for decay) to model the situation described. Be sure to clearly identify both variables in your function.
2. Create a table showing the value of the quantity Q for the first 10 units of time (either years, months, weeks, or hours) of growth or decay.

c. Make a graph of the exponential function.

The population of a town with an initial population of 60,000 grows at a rate of 2.5% per year.

The number of restaurants in a city that had 800 restaurants in 2013 Increases at a rate of 3% per year.

29. A privately owned forest that had 1 million acres of old growth is being clear cut at a rate of 7% per year.

30. A town with a population of 10,000 loses residents at a rate of 0.3% per month because of a poor economy. 31. The average price of a home in a town was $175,000 in 2013, but some prices are rising by 5% per year.

32. A certain drug breaks down in the human body at a rate of 15% per hour. The initial amount of the drug in the bloodstream is 8 milligrams. 33. Your starting salary at a new Job is $2000 per month, and you get annual raises of 5% per year. 34. You hid 100,000 rubles in a mattress at the end of 1991, when they had a value of $10,000. However, the value of the ruble against the dollar then fell 50% per year.