Question

Samantha won a trip to Europe in a contest she had entered. Rather than take the trip, she opted to take the cash value of the prize and put it in a savings account she uses as a college fund. She plans to keep this money in the college fund and let it earn interest for 8 years. At the end of 8 years, she’ll use the total balance to help pay for tuition at law school. The equation below represents the total dollars, f(x)f(x), in her college fund after xx years. The domain for the function that represents the amount of time the money will be in the college fund is 0≤x≤80≤x≤8. The range for the function that represents the amount of money that is in the college fund is 0≤f(x)≤________

a) f(x)≤8
b) f(x)≤x
c) f(x)≤[infinity]
d) f(x)≤________

Answer 1

The correct range for the function representing money in the college fund is from zero to infinity since there's no upper limit specified, which indicates the potential for indefinite growth through compound interest.

Step-by-step explanation:

The range for the function f(x) representing the amount of money in Samantha's college fund after x years cannot be less than zero because we cannot have a negative amount of money in a savings account. Since there is no given upper limit provided in the function, we infer the range of f(x) as the amount of money in the account can theoretically grow indefinitely through compound interest. Therefore, the correct option to fill in the blank (0≤f(x)≤________) would be c) f(x)≤[infinity].