An artificial pond is stocked with an initial population of 2,500 fish. the engineers estimate a 24% decline in the fish population over time without restocking or effects of fishing. the following function models the population, where x is the number of years since the pond was made. f(x) = 2,500(0.76)x

the mathematical range of the function is y > 0. which statement describes how the reasonable range compares to the mathematical range?

the reasonable range has a minimum value of 2,500.
the reasonable range has a maximum value of 2,500.
the reasonable range has a reasonable minimum that cannot be determined.
the reasonable range has a reasonable maximum that cannot be determined.

The reasonable range has a maximum value of 2,500.

Step-by-step explanation:

Notice that the maximum population of fish occurs at the beginning of the study; in other words when time equals zero (x = 0).

We can evaluate our function at x=0 to check how the reasonable range compares with the mathematical range:

Since the fish population is decreasing, it can be never be more than 2,500; therefore the reasonable range has a maximum value of 2,500.

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step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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