water is pumped into a tank at a rate of r(t) and is draining from the tank at a rate of d(t), each in…

water is pumped into a tank at a rate of r(t) and is draining from the tank at a rate of d(t), each in gallons per minute. which expression would indicate that the amount of water in the tank is increasing? r(t) - d(t) > 0 r(t) - d(t) < 0 r(t) - d(t) < 0 r(t) - d(t) > 0

water is pumped into a tank at a rate of r(t) and is draining from the tank at a rate of d(t), each in gallons per minute. which expression would indicate that the amount of water in the tank is increasing? r(t) - d(t) > 0 r(t) - d(t) < 0 r(t) - d(t) < 0 r(t) - d(t) > 0

Answer

Answer:

D. $R(t)-D(t)>0$

Explanation:

Step1: Define net - rate function

Let $W(t)$ be the amount of water in the tank at time $t$. The rate of change of the amount of water in the tank is given by $W'(t)=R(t)-D(t)$ according to the net - rate concept (the rate of inflow minus the rate of outflow).

Step2: Determine when $W(t)$ is increasing

A function $y = W(t)$ is increasing when its derivative $W'(t)>0$. Since $W'(t)=R(t)-D(t)$, the amount of water in the tank is increasing when $R(t)-D(t)>0$.