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)=49(3)−x4, find the revenue if 16 units are sold. Round to two decimal places.

Answer 1

To calculate the total revenue for 16 units sold with a unit price function p(x)=49(3)−x/4, we substitute x with 16 to get the revenue approximately $9.68, rounded to two decimal places.

Step-by-step explanation:

The question involves finding the total revenue generated by selling a certain number of units, using a revenue function. Given the revenue function R(x) = x ⋅ p(x), where p(x) is the unit price and x is the number of units sold, we are asked to calculate the total revenue for 16 units sold. The unit price function is given as p(x)=49(3)−x⁄4. To find the revenue when 16 units are sold, we substitute x with 16:

R(16) = 16 ⋅ p(16)

p(16) = 49(3)−16⁄4 = 49 ⋅ 3−4 = 49 ⋅ 1⁄81 ≈ 0.60493827

R(16) = 16 ⋅ 0.60493827 ≈ 9.67901232 dollars

Therefore, the revenue when 16 units are sold is approximately $9.68, rounded to two decimal places.