Question

The growth of a population of mountain lions can be described by the function f(x) = 500(1.015)^x, where x is the number of years after the first census. How do the mathematical domain and range compare to the reasonable domain and range? Check all that apply.

a) The mathematical and reasonable domains are identical.

b) The mathematical domain is the set of real numbers, while the reasonable domain only includes real numbers greater than or equal to 0.

c) The mathematical domain is the set of real numbers, while the reasonable domain cannot include fractional values.

d) The mathematical range contains all real numbers, while the reasonable range contains all real numbers greater than 0.

e) The mathematical range has a minimum value greater than 0, while the reasonable range is limited to whole numbers and has a minimum value greater than or equal to 500.

Answer 1

The mathematical domain includes all real numbers, while the reasonable domain is limited to real numbers greater than or equal to 0. The mathematical range includes all real numbers, while the reasonable range is limited to positive values greater than or equal to the initial population.

Step-by-step explanation:

The mathematical domain of the function f(x) = 500(1.015)^x is the set of all real numbers. This means that the function can be evaluated for any real number value of x. In contrast, the reasonable domain of the function would be limited to real numbers greater than or equal to 0, since it represents the number of years after the first census. Therefore, option b) - The mathematical domain is the set of real numbers, while the reasonable domain only includes real numbers greater than or equal to 0 - is correct.

The mathematical range of the function contains all real numbers. However, the reasonable range in the context of population growth of mountain lions would be limited to positive values, as the population cannot be negative. Additionally, the minimum value of the reasonable range would be greater than or equal to the initial population of 500. Therefore, option e) - The mathematical range has a minimum value greater than 0, while the reasonable range is limited to whole numbers and has a minimum value greater than or equal to 500 - is correct.