Question

A large koi pond is filled from a garden hose at the rate of 12 gal/min. Initially, the pond contains 200 gal of water.

Answer 1

a) The linear function that models the amount of water after t minutes is given by:

$V(t) = 200 + 12t$

b) It takes 92 minutes to completely fill the pond.

Item a:

• Initially, the pond contains 200 gal of water, that is, the linear function has a y-intercept of 200.
• Filled at a rate of 12 gallons per minute, thus the linear function has a slope of 12.

Then, the function is:

$V(t) = 200 + 12t$

Item b:

It takes t minutes to fill the pond, t is found for which:

$V(t) = 1304$

Then

$200 + 12t = 1304$

$12t = 1104$

$t = \frac{1104}{12}$

$t = 92$

It takes 92 minutes to completely fill the pond.

A similar problem is given at brainly.com/question/16302622