Suppose that a company introduces a new computer game in a city using television advertisements. Surveys show that P% of the target audience buy the game after x ads are broadcast, satisfying the equation below. Complete parts (a) through (d). P(x)= 100 1+51e-0.13x a) What percentage buy the game without seeing a TV ad (x=0)? (Type an integer or a decimal rounded to the nearest tenth as needed.)
Suppose that a company introduces a new computer game in a city using television advertisements. Surveys show that P% of the target audience buy the game after x ads are broadcast, satisfying the equation below. Complete parts (a) through (d). P(x)= 100 1+51e-0.13x a) What percentage buy the game without seeing a TV ad (x=0)? (Type an integer or a decimal rounded to the nearest tenth as needed.)
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3SE: What is regression analysis? Describe the process of performing regression analysis on a graphing...
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![#### Marketing Impact Analysis on Computer Game Sales
**Scenario:**
A company introduces a new computer game in a city using television advertisements. Surveys indicate that P% of the target audience buys the game after x ads are broadcasted, following the equation below. Complete parts (a) through (d).
\[ P(x) = \frac{100}{1 + 51e^{-0.13x}} \]
---
**Task (a): Determine the buy rate without TV ads**
*Question:*
a) What percentage of the audience buys the game without seeing a TV advertisement (x = 0)?
\[ \boxed{\_\_\_} \% \]
*(Note: Type an integer or a decimal rounded to the nearest tenth as needed.)*
---
**Explanation of the equation and parameters:**
- **P(x)**: Percentage of the target audience that buys the game after viewing x number of advertisements.
- **x**: Number of television advertisements broadcasted.
- **100**: Represents the maximum percentage (as a proportion of the total target audience) who could buy the game.
- **51**: A scaling factor that adjusts the curve of the equation.
- **\(e^{-0.13x}\)**: An exponential decay function representing the decreasing marginal effect of each additional ad.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febbbc1cc-ba98-4671-a28a-276fb59e8560%2Fd96d1cab-b9d7-4828-900b-1cb202899f57%2F5v8zr8d_processed.png&w=3840&q=75)
Transcribed Image Text:#### Marketing Impact Analysis on Computer Game Sales
**Scenario:**
A company introduces a new computer game in a city using television advertisements. Surveys indicate that P% of the target audience buys the game after x ads are broadcasted, following the equation below. Complete parts (a) through (d).
\[ P(x) = \frac{100}{1 + 51e^{-0.13x}} \]
---
**Task (a): Determine the buy rate without TV ads**
*Question:*
a) What percentage of the audience buys the game without seeing a TV advertisement (x = 0)?
\[ \boxed{\_\_\_} \% \]
*(Note: Type an integer or a decimal rounded to the nearest tenth as needed.)*
---
**Explanation of the equation and parameters:**
- **P(x)**: Percentage of the target audience that buys the game after viewing x number of advertisements.
- **x**: Number of television advertisements broadcasted.
- **100**: Represents the maximum percentage (as a proportion of the total target audience) who could buy the game.
- **51**: A scaling factor that adjusts the curve of the equation.
- **\(e^{-0.13x}\)**: An exponential decay function representing the decreasing marginal effect of each additional ad.
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