Question

In Purdue's Chemistry department, the chemists have found that in a water based solution containing 1616 grams of certain undissolved chemicals, the rate of change of the amount of chemicals dissolved in the solution is proportional to the amount of the undissolved chemicals. Let Q(t)Q(t) (in grams) be the amount of dissolved chemicals at time tt and let kk be the positive proportionality constant. The differential equation describing the given situation is:

Answer 1

The differential equation describing the given situation is dQ/dt = k( 16 - Q )

Explanation:

Given the data in the question;

Initially, the water based solution contains 16 grams of undissolved chemicals;

Assume Q(t) is the amount of dissolved chemical at time L

then the amount of undissolved chemicals at time t is ( 16 - Q)

The rate of change of amount of chemicals dissolved in the solution is proportional to the amount of undissolved chemicals

this means;

dQ/dt ∝ ( 16 - Q)

dQ/dt = k( 16 - Q )

where k is the positive proportionality constant.

Therefore, The differential equation describing the given situation is dQ/dt = k( 16 - Q )