Question

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.

Which statement describes how the reasonable domain compares to the mathematical domain?

1The reasonable domain is restricted to integers.
2The reasonable domain is restricted to positive real numbers.
3The reasonable domain has a minimum value of 1,500.
4The reasonable domain has a maximum value of 1,500.

Answer 1

B) the reasonable domain is restricted to positive real numbers

Explanation:

Answer 2

2. The reasonable domain is restricted to positive real numbers.

Explanation:

The variable "x" is time in years from when the experiment began. It makes no sense to have negative values of x, as the experiment had not yet begun in negative time.

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I would include x=0 in the domain, too, though you already know the amount of remaining element at x=0 and don't have to use the function to calculate it.

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x might be restricted to integers if you're only measuring the remaining amount once a year.

The maximum value of 1500 applies to the *range* of the function, not its domain.

The minimum value of 1500 has nothing to do with anything.