Question

When full, the volume of water in a fish pond is 657 gallons. Due to a leak in the pond, the volume of water in the pond is decreasing at a rate of 0.8% per minute. If the amount of water in the pond continues to decrease at this rate, create a function, f (x), to model this situation.

Answer 1

When the rate of change is proportional to the amount present, the amount can be modeled using an exponential function. When the decrease is 0.8% per minute, the multiplier is 0.992 each minute. If we let x represent minutes since the pond was full, the volume can be modeled by

`f(x)=657\cdot 0.992^(x)`

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The exponential factor is 1 when x=0, so the initial volume can be used as the multiplier for that factor. There are other ways to express the function, but this is the simplest to obtain from the given data.