Water is being pumped into a pool at a rate of 150 gallons per day, and is evaporating at a rate of 0.2% per day. Which is the differential equation for the amount, A, of gallons of water in the pool as a function of time, t, in days?

Question

Quizplus · Accepted Answer

Let's denote the amount of water in the pool by A. 
The rate at which water is being pumped into the pool is 150 gallons per day. 
The rate at which water is evaporating from the pool is 0.2% per day.

Therefore, the differential equation for the amount, A, of gallons of water in the pool as a function of time, t, in days is:

$\frac{dA}{dt} = 150 - 0.002A$

This is because the change in the amount of water in the pool (dA/dt) is equal to the inflow (150 gallons per day) minus the outflow (0.2% of the current amount of water in the pool, which is 0.002A).

Thus, the correct choice is D.

Water Is Being Pumped into a Pool at a Rate