Question

The revenue function is given by R(x) = x ⋅ p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x) = 41(4⁻ˣ/⁶), find the revenue if 12 units are sold. Round to two decimal places.

Answer 1

Upon calculating the unit price for 12 units as $2.5625 and multiplying by 12, the total revenue from selling 12 units is found to be $30.75.This result is obtained by evaluating the revenue function R(x) for the given number of units sold.

Step-by-step explanation:

To calculate the revenue for 12 units sold when the revenue function is given by R(x) = x · p(x) and the unit price function is p(x) = 41(4⁻¹⁶), we need to plug x=12 into the price function and then multiply by the number of units sold to get the total revenue.

First, calculate the unit price for 12 units:

p(12) = 41(4⁻¹⁶¹⁲) = 41(4⁻²) = 41(1/16) = 41/16 = 2.5625

Now, calculate the total revenue by multiplying the unit price by the number of units sold:

R(12) = 12 · 2.5625 = 30.75

The total revenue from selling 12 units is $30.75, rounded to two decimal places.

The revenue, when 12 units are sold with the given unit price function, is approximately $30.75,This result is obtained by evaluating the revenue function R(x) for the given number of units sold.