The function 
S = 50,000e−0.2x
 models sales decay for a given product. The variable S represents the monthly sales and the variable x represents the number of months that have passed since the promotional campaign ended.
If 9 months have passed since the promotional campaign ended, then 
x = 
 
Incorrect: Your answer is incorrect.
 can be substituted into the given function to compute the sales, S, for this product at this point in time.

Substitute this x-value in and simplify the exponent for e.
S	 = 	50,000e−0.2x

 = 	50,000e
 
Incorrect: Your answer is incorrect.

Since S is measured in dollars, round the answer to the nearest cent (hundredth). Nine months after the promotional campaign ends, the sales are predicted to be $ 
 
Incorrect: Your answer is incorrect.
 .


We are given the function $ S = 50,000 e^{-0.2x} $, where $ S $ represents the sales and $ x $ represents the number of months that have passed since the promotional campaign ended. We are tasked with finding $ S $ when $ x = 9 $ months.

### Step 1: Substitute $ x = 9 $ into the equation.

\[
S = 50,000 e^{-0.2 \times 9}
\]

Simplify the exponent:

\[
S = 50,000 e^{-1.8}
\]

### Step 2: Approximate $ e^{-1.8} $.

Using a calculator or approximation:

\[
e^{-1.8} \approx 0.165298
\]

### Step 3: Multiply by 50,000.

Now calculate the sales:

\[
S = 50,000 \times 0.165298 = 8,264.90
\]

### Final Answer:

The predicted sales after 9 months are approximately **\$8,264.90**.

Would you like more details on any step, or have any questions?

### Relative Questions:
1. What does the function suggest about the long-term sales trend?
2. How does the decay constant, $-0.2$, affect the sales over time?
3. What are some methods to calculate the value of $ e^{-1.8} $ without a calculator?
4. Can the function be modified to model a different product with a slower decay rate?
5. What would sales be after 12 months using the same model?

### Tip:
When dealing with exponential decay, always check the units of the decay constant to understand the time scale of the process.

The function S = 50,000e−0.2x models sales decay for a given product. The variable S represents the monthly sales and the variable x represents the number of months that have passed since the promotional campaign ended. If 9 months have passed since the promotional campaign ended, then x = Incorrect: Your answer is incorrect. can be substituted into the given function to compute the sales, S, for this product at this point in time. Substitute this x-value in and simplify the exponent for e. S = 50,000e−0.2x = 50,000e Incorrect: Your answer is incorrect. Since S is measured in dollars, round the answer to the nearest cent (hundredth). Nine months after the promotional campaign ends, the sales are predicted to be $ Incorrect: Your answer is incorrect.

Learn how to calculate the sales decay using the exponential model S = 50,000e−0.2x. This example covers substituting x = 9 months into the equation and simplifying the exponential term. The final sales value is calculated to the nearest cent, with a result of $8,264.90 after 9 months. Suitable for high school students in Grades 10-12.

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