Questions: An arcade sells video games and determines that x=40(1-e^(-p/8)), where x is the number of video games demanded for a unit price p. Step 1 of 4 : Determine the quantity demanded when p=11 per game. Round your answer to the nearest whole number.

An arcade sells video games and determines that x=40(1-e^(-p/8)), where x is the number of video games demanded for a unit price p.
Step 1 of 4 : Determine the quantity demanded when p=11 per game. Round your answer to the nearest whole number.

Transcript text: Chapter 6 SmartBook - 24FA-ACC120-N884: Prin of Financial Accounting learn.hawkeslearning.com Save \& Exit Certify Lesson: 5.6 Elasticity of Demand PAOLA AGUILAR MARTINEZ Question 1 of 14, Step 1 of 4 $0 / 25$ Correct 5 An arcade sells video games and determines that $x=40\left(1-e^{-\frac{p}{8}}\right)$, where $x$ is the number of video games demanded for a unit price $p$. Step 1 of 4 : Determine the quantity demanded when $p=\$ 11$ per game. Round your answer to the nearest whole number. Answer Keypad Keyboard Shortcuts video games

Solution

Solution Steps

To determine the quantity demanded when $ p = \$11 $, substitute $ p = 11 $ into the given demand equation $ x = 40\left(1-e^{-\frac{p}{8}}\right) $. Calculate the expression to find the value of $ x $ and round it to the nearest whole number.

Step 1: Substitute the Given Price into the Demand Equation

Substitute $ p = 11 $ into the demand equation: \[ x = 40 \left(1 - e^{-\frac{11}{8}}\right) \]

Step 2: Calculate the Exponential Term

Calculate the exponential term: \[ e^{-\frac{11}{8}} \approx 0.2466 \]

Step 3: Compute the Quantity Demanded

Substitute the value of the exponential term back into the equation: \[ x = 40 \left(1 - 0.2466\right) = 40 \times 0.7534 \approx 30.136 \]

Step 4: Round to the Nearest Whole Number

Round $ x $ to the nearest whole number: \[ x \approx 30 \]