on a certain route, an airline carries 9000 passengers per month, each paying $150. a market survey…

on a certain route, an airline carries 9000 passengers per month, each paying $150. a market survey indicates that for each $1 decrease in the ticket price, the airline will gain 40 passengers.\na. express the number of passengers per month, n, as a function of the ticket price, x.\nb. express the monthly revenue for the route, r, as a function of the ticket price, x.\na. n(x) =

on a certain route, an airline carries 9000 passengers per month, each paying $150. a market survey indicates that for each $1 decrease in the ticket price, the airline will gain 40 passengers.\na. express the number of passengers per month, n, as a function of the ticket price, x.\nb. express the monthly revenue for the route, r, as a function of the ticket price, x.\na. n(x) =

Answer

Explanation:

Step1: Find the change in price

The initial price is $150. The change in price from the initial price is $150 - x$.

Step2: Calculate the number of additional passengers

Since for each $1 decrease in price, 40 more passengers are gained, the number of additional passengers is $40(150 - x)$.

Step3: Express the number of passengers as a function of price

The initial number of passengers is 9000. So, $N(x)=9000 + 40(150 - x)$. Simplify this expression: [ \begin{align*} N(x)&=9000+40\times150-40x\ &=9000 + 6000-40x\ &=15000-40x \end{align*} ]

Step4: Calculate the monthly - revenue function

The revenue $R$ is the product of the number of passengers $N(x)$ and the ticket price $x$. So, $R(x)=x\times N(x)=x(15000 - 40x)=15000x-40x^{2}$.

Answer:

a. $N(x)=15000 - 40x$ b. $R(x)=15000x-40x^{2}$