Final answer:
None of the given function options correctly represent your best friend's account balance after x weeks according to the balance data in the table. The balance increases at a rate of $15 per week, starting from $50, which would be represented by the function B(x) = 50 + 15x, but this function is not listed among the choices.
Step-by-step explanation:
To determine which function represents your best friend's account balance after x weeks, we need to analyze the given table of balances. We are given the balances for weeks 1, 4, and 8, which are $50, $95, and $155, respectively.
Since the balance is increasing by the same amount each week, we are looking for a linear function of the form B(x) = mx + b, where m is the slope (the weekly deposit) and b is the initial balance.
Looking at the table, we can see that the balance increases by $45 over 3 weeks from week 1 to week 4 ($95 - $50 = $45), which means the weekly deposit m is $15 per week ($45 / 3 weeks = $15/week). Therefore, we can rule out any options that do not have a slope of $15. Similarly, since the balance started at $50 in week 1, the initial balance b is $50.
The correct function representing your best friend's account balance after x weeks is B(x) = 50 + 15x. However, this option is not presented among the choices. The closest match by the given slope would be option B) B(x) = 50 + 10x, but it has a slope of $10 per week, not $15. Therefore, the information provided in the question or the answer choices might have an error since none of the options correctly represent the table of balances provided.