A chemical concentration (in grams per liter) in a well-mixed tank changes with time…

MATHEMATICS · Multi-part · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

A chemical concentration

C

(in grams per liter) in a well-mixed tank changes with time

t

(in minutes) according to the differential equation

\frac{dC}{dt}=\frac{3t-6}{t(t+2)}, \qquad C(1)=5.

Use this model to answer the questions below. (a) Write the differential equation in differential form with all terms involving

C

on one side and all terms involving

t

on the other. (b) Integrate to obtain an implicit relation between

C

and

t

. (c) Apply the initial condition to solve for the constant of integration. (d) Determine the time

t>1

at which the concentration first reaches

8\text{ g/L}

. Express your answer in exact form.