A certain element has a half-life of 69 years. An experiment starts with 1,500 grams of the element. The amount of the element remaining x years after the experiment began can be modeled with the function f(x) = 1,500(2)–x/69. The mathematical domain of the function is all real numbers.
Answer
A
The reasonable domain is restricted to integers.
B
The reasonable domain is restricted to positive real numbers.
C
The reasonable domain has a minimum value of 1,500.
D
The reasonable domain has a maximum value of 1,500.
Explanation
The input x represents the number of years elapsed since the experiment began, so it cannot be negative. Elapsed time can include fractions of a year, so x is not restricted to integers. Thus the reasonable domain is positive real numbers (with the starting time x = 0 also representing the experiment’s beginning).
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