Chapter 13.4, Problem 59E

To determine

To find whether the spill reach a well dug $2300$ meters away.

Answer to Problem 59E

  $2000$ Meters.

Explanation of Solution

Given:

After one year the chemical has spread $1200$ meters and after two years the chemical has spread $480$ meters more and by the end of third year it has reached an $192$ additional meters.

Calculation:

The pattern describes the geometric series as the common ratio is same $r=\frac{192}{480}=\frac{480}{1200}=0.4$

The first term $a_1=1200$

The spill will spread until it reaches the sum of the series-

  $\begin{array}{l}S=\frac{a_1}{1-r}\\ S=\frac{1200}{1-0.4}=2000\end{array}$

This means that the spill will spread no more than $2000$ metersaway.