Question

Evaluate the following expression for kequals4 and nequals8.
18 comma 000 left parenthesis 1 plus StartFraction 0.10 Over k EndFraction right parenthesis Superscript kn
Question content area bottom
Part 1
18 comma 000 left parenthesis 1 plus StartFraction 0.10 Over k EndFraction right parenthesis Superscript kn
equals
  
enter your response here
​(Do not round until the final answer. Then round to two decimal places as​ needed.)

Answer 1

To evaluate the expression \( 18,000 \left( 1 + \frac{0.10}{k} \right)^{kn} \) for \( k = 4 \) and \( n = 8 \), we will follow these steps:

1. Substitute \( k \) and \( n \) into the expression.
2. Calculate \( \frac{0.10}{k} \).
3. Solve for the power \( kn \).
4. Evaluate the entire expression.

Let's go through these steps:

### Step 1: Substitute \( k \) and \( n \)

Given \( k = 4 \) and \( n = 8 \):

\[
kn = 4 \times 8 = 32
\]

### Step 2: Calculate \( \frac{0.10}{k} \)

Now, substituting \( k \):

\[
\frac{0.10}{k} = \frac{0.10}{4} = 0.025
\]

### Step 3: Substitute into the expression

Now we substitute back into the original expression:

\[
18,000 \left( 1 + 0.025 \right)^{32}
\]

This simplifies to:

\[
18,000 \left( 1.025 \right)^{32}
\]

### Step 4: Calculate \( (1.025)^{32} \)

Now, we will calculate \( (1.025)^{32} \):

\[
(1.025)^{32} \approx 2.208040
\]

### Step 5: Multiply by 18,000

Now, we multiply this value by 18,000:

\[
18,000 \times 2.208040 \approx 39,744.72
\]

### Final Answer

Thus, rounding to two decimal places, our final answer is:

\[
\boxed{39,744.72}
\]