Answer:
The flow rate at t=4.5 is approximately 11.
Step-by-step explanation:
We have tabulated data that relates volume V with time t.
We are asked to determine the rate of flow (variation of volume in time, first derivative dV/dt) at t=4.5.
The centered-difference formula let us calculate an approximation of the first derivative of a function at a specific point, from the values of the function:
[tex]f'(x)\approx\dfrac{f(x+h)-f(x-h)}{2h}[/tex]
The value of x in this case is 4.5, as it is the point in which we want to calculate the rate of flow.
The value of h is the step used in the table. In this case, h=0.5.
Then the values we need from the function are:
[tex]f(x+h)=f(4.5+0.5)=f(5)=65\\\\f(x-h)=f(4.5-0.5)=f(4)=44[/tex]
We now can calculate the first derivative approximation with the centered-difference formula
[tex]f'(4.5)\approx\dfrac{f(5)-f(4)}{2*0.5}=\dfrac{65-44}{1}\\\\f'(4.5)\approx11[/tex]
