Question

Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function that best represents Samantha's account and how much does she have in savings after 5 years? Round your answer to the nearest dollar.

Hint: Use the formula, f(x) = P(1 + r)x.

f(x) = 500(1.4)x, $2,689
f(x) = 500(0.04)x, $512
f(x) = 500(1.04)x, $608
f(x) = 500(1.04)x, $5

Answer 1

So based on the given problem above, and the given formula, the function that would best represent Samantha's account would be this: f(x) = 500 (1.04)^x
Since P is amount and r is the interest rate so P is 500 and r is 0.04.
f(x)= P(1 + r)x.
f(x) = 500 (1 + 0.04)^x
f(x) = 500 (1.04)^x
Now, solve for it:
f(x) = 500 (1.04)^5
f(x) = 500 (1.21665)
f(x) = 608
Therefore, the answer would be the third option. Hope this helps.