Question

question 13 (essay worth 10 points) (hc) a band is performing at a concert venue. the performance fee is $3,000, and each ticket costs $50. the linear function r(x)=50x + 3,000 models the total revenue, r(x), in dollars, for a given number of tickets sold, x. part a: if the band wants to earn $10,000 in revenue, how many tickets need to be sold? show all necessary steps (4 points) part b: what are the domain and range of the given function, r(x)? (2 points) part c: if the concert venue is limited to 500 people, how does that change the domain and range of the function? (4 points)

Explanation:

Step1: Set up equation for Part A

$10000 = 50x+3000$

Step2: Solve for x

$50x=10000 - 3000=7000$, $x = \frac{7000}{50}=140$

Step3: Find domain and range for Part B

Domain: $x\geq0$ (non - negative tickets), Range: $r(x)\geq3000$

Step4: Adjust for Part C

Domain: $0\leq x\leq500$, Range: $3000\leq r(x)\leq50\times500 + 3000=28000$

Answer:

Part A: 140 tickets
Part B: Domain: $x\geq0$, Range: $r(x)\geq3000$
Part C: Domain: $0\leq x\leq500$, Range: $3000\leq r(x)\leq28000$