A water tank is filled at a rate of r(t) liters per minute (where t is the time in minutes). What does int_(1)^(7)r^(')(t)dt represent? Choose 1 answer: (A) The rate at which the tank was filled at t=7. B The amount of water filled between t=1 and t=7. (C) The change in the rate of filling between t=1 and t=7. (D) The average rate of filling between t=1 and t=7.

Question

A water tank is filled at a rate of  r(t) liters per minute (where  t is the time in minutes). What does  int_(1)^(7)r^(')(t)dt represent? Choose 1 answer: (A) The rate at which the tank was filled at  t=7. B The amount of water filled between  t=1 and  t=7. (C) The change in the rate of filling between  t=1 and  t=7. (D) The average rate of filling between  t=1 and  t=7.

Bytelearn · Accepted Answer

Understand Rate of Change Integral: Understand the integral of a rate of change. The integral of a rate of change function, in this case r'(t), over an interval [a, b] gives the total change in the quantity that the rate of change function is describing over that interval.Apply Fundamental Theorem: Apply the Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus states that if F is an antiderivative of f on an interval [a, b], then the integral from a to b of f(t) dt is F(b) - F(a). Here, r(t) is the antiderivative of r'(t), so the integral from 1 to 7 of r'(t) dt gives r(7) - r(1).Interpret Result: Interpret the result in the context of the problem. Since r(t) represents the volume of water in the tank at time t, r(7) - r(1) represents the change in volume of the water in the tank from time t=1 to t=7. This is the amount of water that has been filled into the tank during this time interval.

Full solution

More problems from Interpreting Linear Expressions

Related topics