Question 145951 • FL-1200330-Algebra 2 Sem 1 - Flex
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.The mathematical and reasonable domains are identical.The mathematical domain is the set of real numbers, while the reasonable domain only includes real numbers greater than or equal to 0.The mathematical domain is the set of real numbers, while the reasonable domain cannot include fractional values.The mathematical range contains all real numbers, while the reasonable range contains all real numbers greater than 0.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
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.
Explanation
Since x is years after the first census, the reasonable domain is x ≥ 0; the function’s mathematical domain is all real numbers, so B is correct. For real x, 500(1.015)^x is always positive, while a real population is counted in whole numbers and cannot be less than the initial 500 lions. Thus E describes the reasonable range and the positive mathematical range. Strictly, the mathematical range has no attained minimum; its values approach 0 as x decreases.
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