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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

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