Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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.
(a) Find a linear function V that models the volume of water in the pond at any time t.
(b) If the pond has a capacity of 1304 gal, how long does it take to completely fill the pond?

Sagot :

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

[tex]V(t) = 200 + 12t[/tex]

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:

[tex]V(t) = 200 + 12t[/tex]

Item b:

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

[tex]V(t) = 1304[/tex]

Then

[tex]200 + 12t = 1304[/tex]

[tex]12t = 1104[/tex]

[tex]t = \frac{1104}{12}[/tex]

[tex]t = 92[/tex]

It takes 92 minutes to completely fill the pond.

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

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.