Chapter 4.3, Problem 8E

Reminder Round all answers to two decimal places unless otherwise indicated.

Insect Control DDT (dichlorodiphenyltrichloroethane) was used extensively from 1940 to 1970 as an insecticide. It still sees limited use for control of disease. But DDT was found to be harmful to plants and animals, including humans, and its effects were found to be lasting. The amount of time that DDT remains in the environment depends on many factors, but the following table shows what can be expected of 100 kilograms of DDT that has seeped into the soil.

$\begin{array}{l}t=\text{time,}\text{in}\text{years}\\ \text{since}\text{application}\end{array}$	$\begin{array}{l}D=\text{DDT}\text{remaining,}\\ \text{in}\text{kilograms}\end{array}$
$0$	$100.00$
$1$	$95.00$
$2$	$90.25$
$3$	$85.74$

a. Show that the data are exponential.

b. Make a model of D as an exponential function of t.

c. What is the half-life of DDT in the soil? That is, how long will it be before only 50 kilograms of DDT remain?