Question

benjamin invests $400 in a savings account that earns 5% interest each year. which graph shows the balance of benjamins savings y (in dollars) after x years? choose 1 answer:

Explanation:

Step1: Identify initial value

The initial investment is $\$400$, so when $x=0$, $y=400$. This eliminates graphs A and C, which start at $y=300$.

Step2: Identify growth type

This is compound interest, so the balance follows an exponential growth model:
$$y = 400(1 + 0.05)^x = 400(1.05)^x$$
Exponential growth produces a curve that increases at an increasing rate, which matches graph B.

Step3: Verify 1-year balance

Calculate balance after 1 year:
$$y = 400 \times 1.05 = 420$$
Graph B shows a value greater than 400 at $x=1$, consistent with this calculation.

Answer:

B. The graph starting at (0, 400) with an upward-curving line rising to over 600 at x=5