question 7 11:46 7. a pump allows water to flow into a pool at the rate of r(t)=2t liters per minute, where…

question 7 11:46 7. a pump allows water to flow into a pool at the rate of r(t)=2t liters per minute, where t is the time in minutes since the pump was turned on. which of the following defines a function that measures the accumulation of water in the pool during the time - period from t = 1 to t = x as the variable moves along the t - axis as shown in the figure below? f(x)=2x f(x)=1 + 2x f(x)=∫1^x2t dt f(x)=∫0^x2t dt

question 7 11:46 7. a pump allows water to flow into a pool at the rate of r(t)=2t liters per minute, where t is the time in minutes since the pump was turned on. which of the following defines a function that measures the accumulation of water in the pool during the time - period from t = 1 to t = x as the variable moves along the t - axis as shown in the figure below? f(x)=2x f(x)=1 + 2x f(x)=∫1^x2t dt f(x)=∫0^x2t dt

Answer

Explanation:

Step1: Recall the concept of accumulation

The accumulation of a quantity with a rate - function $r(t)$ over the interval $[a,b]$ is given by the definite integral $\int_{a}^{b}r(t)dt$. Here, the rate of water - flow is $r(t) = 2t$ liters per minute, and we want to find the accumulation of water in the pool from $t = 1$ to $t=x$.

Step2: Set up the definite integral

The accumulation function $f(x)$ is given by $f(x)=\int_{1}^{x}2t\ dt$.

Answer:

$f(x)=\int_{1}^{x}2t\ dt$