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.

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

_____

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.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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