Isabella has $1,000 to invest and explores a number of options at her local bank. After learning about her options, she decides to deposit her $1,000 into a high-yield savings account that compounds at an annual rate of 4%, compounded quarterly. The banker tells Isabella that her projected earnings in dollars, P, as a function of time in years, t, can best be represented by the equation P(t) = 1000(1.01)4t. Which of the following graphs best illustrates Isabella's projected earnings over time?
A.
B.
C.
D.
Answer:B
Isabella has $1,000 to invest and explores a number of options at her local bank. After learning about her options, she decides to deposit her $1,000 into a high-yield savings account that compounds at an annual rate of 4%, compounded quarterly. The banker tells Isabella that her projected earnings in dollars, P, as a function of time in years, t, can best be represented by the equation P(t) = 1000(1.01)4t. Which of the following graphs best illustrates Isabella's projected earnings over time?
A. B. C. D.
Explanation: BWe know that Isabella starts with $1,000 in her account, so this eliminates (D). She is earning money from the interest, so the line must have a positive slope, eliminating (C), which has a constant slope. The two best choices are (A) and (B), but in (A) Isabella's money doesn't begin to increase until the 5-year mark, which doesn't make sense-thus (B) is the best choice.