Chapter 1.4, Problem 1TU

TEST YOUR UNDERSTANDING

Suppose we start with $9$ milligrams of pollutant per liter of water, as in the example. Assume that the cleaning process decreases the concentration of pollutant by $30\%$ each hour. What is the pollutant concentration after each of the first $3$ hours?

EXAMPLE 1.9 PURIFYING WATER

Water that is initially contaminated with a concentration of 9 milligrams of pollutant per liter of water is subjected to a cleaning process. The cleaning process is able to reduce the pollutant concentration by 25% each hour. Let $C=C\left(t\right)$ denote the concentration, in milligrams per liter, of pollutant in the water r hours after the purification process begins.

Part 1 What is the concentration of pollutant in the water after 3 hours?

Part2 Compare the results predicted by the verbal description at the end of each of the first 3 hours with those given by the formula $C=9\times {0.75}^t$.

Part 3 The formula given in part 2 is, in fact, the correct one. Use it to find the concentration of pollutant after $4\frac{1}{4}$ hours of cleaning.