Water is poured into a bucket according to the rate F (t) = (t + 7) / (2 + t), and at the same time empties out through a hole in the bottom at the rate E (t) = ln (t + 4) / (t + 2), with both F (t) and E (t) measured in pints per minute. How much water, to the nearest pint, is in the bucket at time t = 5 minutes. You must show your setup but can use your calculator for all evaluations.

Question

Mathematics

Sienna Bond

23 June, 06:35

Water is poured into a bucket according to the rate F (t) = (t + 7) / (2 + t), and at the same time empties out through a hole in the bottom at the rate E (t) = ln (t + 4) / (t + 2), with both F (t) and E (t) measured in pints per minute. How much water, to the nearest pint, is in the bucket at time t = 5 minutes. You must show your setup but can use your calculator for all evaluations.

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Coby · Answer 1

The amount of water in the bucket at t=5, will be estimated as follows:

Assuming that both pipes started running at the same time, the amount of water poured in the bucket at t=5 will be:

F (t) = (t + 7) / (2 + t)

f (5) = (5+7) (2+5)

f (5) = (12) (7)

f (5) = 84

Amount of water drawn from the bucket at t=5 will be:

E (t) = ln (t + 4) / (t + 2)

E (5) = ln (5+4) / (5+2)

E (5) = ln (9) / (7)

Thus the amount of water in the bucket at t=5 will be:

84-ln 9/7

~83.74868557

~83.8