Problem

The demand for a new computer game can be modeled by $p(x)=43-5 \ln x$, for $0 \leq x \leq 800$, where $p(x)$ is the price consumers will pay, in dollars, and $x$ is the number of games sold, in thousands. Recall that total revenue is given by $R(x)=x \cdot p(x)$. Complete parts (a) through (c) below. a) Find $R(x)$. \[ R(x)= \]

Solution

Step 1 :Given the price function $p(x)=43-5 \ln x$, where $p(x)$ is the price consumers will pay, in dollars, and $x$ is the number of games sold, in thousands.

Step 2 :We are asked to find the total revenue function $R(x)$, which is given by $R(x)=x \cdot p(x)$.

Step 3 :Substitute $p(x)$ into the revenue function to get $R(x)=x(43-5 \ln x)$.

Step 4 :\(\boxed{R(x)=x(43-5 \ln x)}\)

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Source: https://solvelyapp.com/problems/27694/

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