Question

an environmental firm is removing pollution from a river bed .they find that the pollution is decreasing at a rate of 5% per month as measured by parts per million.the pollution starts off at a level of 360 parts per million(ppm).(a)what is the pollution level one month after they begin clean up ? use appropriate units.(b)what is the level two months after ?use appropriate units.

Answer 1

Given data:

The given rate deceasing per month is r=5% =0.05.

The initial value of pollution is P=360 parts per million(ppm).

The given time is n=1 month.

(a)

The expression pollution level is,

$P_f=P(1-r)^n$

Substitute the given values in the above expression.

$\begin{gathered} P_f=(360ppm)(1-0.05)^1 \\ =342\text{ ppm} \end{gathered}$

Thus, the final value of pollution after one month is 342 ppm.

(b)

Given data:

The given value of time is n=2.

Substitute given values in the expression for the pollution level.

$\begin{gathered} P_f=(360ppm)(1-0.05)^2 \\ =324.9\text{ ppm} \end{gathered}$

Thus, the final value of pollution after two months is 324.9 ppm.