select the correct answer from each drop - down menu. the function f(x)=500(1 + \\frac{0.015}{4})^{4x}…

select the correct answer from each drop - down menu. the function f(x)=500(1 + \\frac{0.015}{4})^{4x} models the balance in a savings account. the savings account had an initial balance of $500 and compounds at an interest rate of

select the correct answer from each drop - down menu. the function f(x)=500(1 + \\frac{0.015}{4})^{4x} models the balance in a savings account. the savings account had an initial balance of $500 and compounds at an interest rate of

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount (initial balance), $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. In the function $f(x)=500(1 +\frac{0.015}{4})^{4x}$, when $x = 0$ (at the start), $f(0)=500(1+\frac{0.015}{4})^{0}=500\times1 = 500$.

Answer:

The initial balance is $500. The interest rate is $1.5%$ (since $r = 0.015$) and it compounds quarterly (since $n = 4$). So the answers are:

  • Initial balance: $500$
  • Interest rate: $1.5%$
  • Compounding frequency: Quarterly