attempt 1: 10 attempts remaining. the demand for a new online computer game is given by $p(q)=48600…
attempt 1: 10 attempts remaining. the demand for a new online computer game is given by $p(q)=48600 - 11400ln(q)$ for $qgeq1$, where $p(q)$ is the price per game (in dollars) and $q$ is the number of games sold. find the rate of change of the price of the new game when 3800 games have been sold. the price of the new game when 3800 games have been sold is ? by ?
Answer
Explanation:
Step1: Differentiate the price - function
The derivative of a constant is 0, and the derivative of $\ln(q)$ with respect to $q$ is $\frac{1}{q}$. Using the rules of differentiation, if $p(q)=48600 - 11400\ln(q)$, then $p^\prime(q)=\frac{d}{dq}(48600)-11400\frac{d}{dq}(\ln(q))$. Since $\frac{d}{dq}(48600) = 0$ and $\frac{d}{dq}(\ln(q))=\frac{1}{q}$, we have $p^\prime(q)=-\frac{11400}{q}$.
Step2: Evaluate the derivative at $q = 3800$
Substitute $q = 3800$ into $p^\prime(q)$. So $p^\prime(3800)=-\frac{11400}{3800}$. Simplify the right - hand side: $p^\prime(3800)= - 3$.
Answer:
The price of the new game is changing at a rate of - 3 dollars per game when 3800 games have been sold.