Questions: Use a calculator and evaluate A to the nearest cent. A = 15,000 e^0.1 t for t=5,7, and 8 If t=5, A ≈ (Do not round until the final answer. Then round to the nearest hundredth.) If t=7, A ≈ (Do not round until the final answer. Then round to the nearest hundredth.) If t=8, A ≈ (Do not round until the final answer. Then round to the nearest hundredth.)

Use a calculator and evaluate A to the nearest cent. A = 15,000 e^0.1 t for t=5,7, and 8 If t=5, A ≈ (Do not round until the final answer. Then round to the nearest hundredth.) If t=7, A ≈ (Do not round until the final answer. Then round to the nearest hundredth.) If t=8, A ≈ (Do not round until the final answer. Then round to the nearest hundredth.)
Transcript text: Use a calculator and evaluate A to the nearest cent. \[ A=\$ 15,000 e^{0.1 t} \text { for } t=5,7 \text {, and } 8 \] \[ \text { If } \mathrm{t}=5, \mathrm{~A} \approx \$ \] $\square$ (Do not round until the final answer. Then round to the nearest hundredth.) \[ \text { If } \mathrm{t}=\mathrm{7}, \mathrm{~A} \approx \mathrm{\$} \square \] (Do not round until the final answer. Then round to the nearest hundredth.) \[ \text { If } \mathrm{t}=8, \mathrm{~A} \approx \$ \square \] (Do not round until the final answer. Then round to the nearest hundredth.)
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Solution

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Solution Steps

Step 1: Evaluate \( A \) for \( t = 5 \)

The formula for \( A \) is: \[ A = \$15,000 \cdot e^{0.1 t} \] For \( t = 5 \): \[ A = \$15,000 \cdot e^{0.1 \cdot 5} = \$15,000 \cdot e^{0.5} \] Using a calculator, \( e^{0.5} \approx 1.6487 \). Thus: \[ A = \$15,000 \cdot 1.6487 = \$24,730.50 \] Rounded to the nearest cent, \( A \approx \$24,730.50 \).

Step 2: Evaluate \( A \) for \( t = 7 \)

For \( t = 7 \): \[ A = \$15,000 \cdot e^{0.1 \cdot 7} = \$15,000 \cdot e^{0.7} \] Using a calculator, \( e^{0.7} \approx 2.0138 \). Thus: \[ A = \$15,000 \cdot 2.0138 = \$30,207.00 \] Rounded to the nearest cent, \( A \approx \$30,207.00 \).

Step 3: Evaluate \( A \) for \( t = 8 \)

For \( t = 8 \): \[ A = \$15,000 \cdot e^{0.1 \cdot 8} = \$15,000 \cdot e^{0.8} \] Using a calculator, \( e^{0.8} \approx 2.2255 \). Thus: \[ A = \$15,000 \cdot 2.2255 = \$33,382.50 \] Rounded to the nearest cent, \( A \approx \$33,382.50 \).

Final Answer

\[ \boxed{ \begin{aligned} &\text{If } t = 5, \quad A \approx \$24,730.50 \\ &\text{If } t = 7, \quad A \approx \$30,207.00 \\ &\text{If } t = 8, \quad A \approx \$33,382.50 \end{aligned} } \]

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