leela invests $500 at 4.5% interest according to the equation $v_{l}=500(1.045)^{t}$, where $v_{l}$ is the…

leela invests $500 at 4.5% interest according to the equation $v_{l}=500(1.045)^{t}$, where $v_{l}$ is the value of the account after $t$ years. adele invests the same amount of money at the same interest rate, but begins investing two years earlier according to the equation $v_{a}=500(1.045)^{t + 2}$. the total value of adeles account is approximately what percent of the total value of leelas account at any time, $t$?\n101.3%\n104.5%\n109.0%\n109.2%

leela invests $500 at 4.5% interest according to the equation $v_{l}=500(1.045)^{t}$, where $v_{l}$ is the value of the account after $t$ years. adele invests the same amount of money at the same interest rate, but begins investing two years earlier according to the equation $v_{a}=500(1.045)^{t + 2}$. the total value of adeles account is approximately what percent of the total value of leelas account at any time, $t$?\n101.3%\n104.5%\n109.0%\n109.2%

Answer

Explanation:

Step1: Set up the ratio

We want to find what percent $V_e$ is of $V_l$. The ratio is $\frac{V_e}{V_l}$. Substitute the given equations: $\frac{500(1.045)^{t + 2}}{500(1.045)^{t}}$.

Step2: Simplify the ratio

Using the exponent - rule $\frac{a^m}{a^n}=a^{m - n}$, we have $\frac{500(1.045)^{t+2}}{500(1.045)^{t}}=(1.045)^{(t + 2)-t}=(1.045)^{2}$.

Step3: Calculate the value

$(1.045)^{2}=1.045\times1.045 = 1.092025$.

Step4: Convert to percentage

To convert the decimal to a percentage, multiply by 100. So $1.092025\times100 = 109.2025%\approx109.2%$.

Answer:

109.2%