A lake initially contains of a certain pollutant

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A lake initially contains

120\text{ mg}

of a certain pollutant. The rate at which the pollutant mass

M

(in milligrams) changes is proportional to

M

, and after

3

days the amount of pollutant has decreased to

85\text{ mg}

. (a) Determine the value of the proportionality constant

k

(including its sign and units) for the pollutant’s decay. (b) Using the value of

k

obtained in part (a), calculate the number of days required for the pollutant mass to decrease to

30\text{ mg}

. Round your answer to one decimal place. (c) Suppose environmental regulations require the pollutant level to fall below

10\text{ mg}

. Estimate, to the nearest day, how long after the initial measurement regulators must wait before the lake meets this standard.