Chapter 6.4, Problem 74E

The value of a car decreases each year. The rate at which the value decreases is called depreciation and is a represented by a percentage. For Alina buys a car for $25,000, and the depreciation rate is 25%. That means that her car’s value goes down by 25% each year. The value can be represented by the function V(y)=25000(0.75)^v, where V represents the value of her car and y represents the number of years that she owns a car. Find the depreciated value of her car if she keeps it for 5 years. In other words, evaluate: V(5)=25000(0.75)^5, rounding to the proper decimal place for money.

A 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate of 10 gal/min and the resulting uniform mixture is removed from the tank at the same rate. Derive an expression for the amount of dye in the tank as a function of time. Find the time t at which the tank contains 26% dye solution.

4) A typical cup of coffee contains 100 mg of caffeine. Every hour, approximately 16% of the amount of caffeine in the body is metabolized and eliminated. Let C represent the amount of caffeine in the body in mg and let t represent the number of hours since a typical cup of coffee was consumed. (a) Write an equation where C is a function of t for a typical cup of coffee. (b) How much caffeine is left in the body after 3 hours? (c) Suppose an individual cannot sleep unless she has less than 50 mg of caffeine in her blood. How many hours after drinking coffee must she wajt until she is able to fall asleep?