Watson is filling a pool with water. Suppose the flow rate r(t) = 5 + 2sin(t) gi

Question

Watson is filling a pool with water. Suppose the flow rate r(t) = 5 + 2sin(t) gives the gallons per second at which the water is flowing into the pool at time t seconds after he turns on the faucet. We are going to make a new function, f(t)= integral_t=5^t [5 + 2 sin (t)]dt. First, let's try to figure out why this is even a function. Use "show work" to answer the following: a. What does the function f input? What does it output? b. Draw a graph of r(t). c. Estimate f(t) for t = 5, 10, 15, and 20. d. Use these estimates to sketch a graph of f (t). e. On the same set of axes, sketch also a graph of a new function g(t)= integral_t=0^t [5 + 2 sin (t)] dt. f. Discuss the relationship between the functions f and g.

Explanation / Answer

a. f inputs the flow rate and outputs the amount of water filled in the pool from time t=5 to time t=t

b. Search on google 'graph of 5+2sin(t) and you shall get the answer

c. The integral of 5+2sin(t) from 5 to t = 5t-2cos(t)-24.43
For t=5, it is equal to 0
For t=10, it is equal to 27.25
for t=15, it is equal to 52.09
For t=20, it is equal to 74.75

d. google for 'graph of '-2cost(t)-19.43

e. This function is equal to: 5-2cost(t) +2. Therefore, google for 'graph of 7-2cos(t)'

f. g represents the total volume since time t=0, while f is from time t=5

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