Answer:
The required equation is: [tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}=17[/tex]
Step-by-step explanation:
Consider the provided information.
Let x represents tickets sold.
A theme park charges a flat fee of $500 for group bookings of more than 25 tickets, plus $20 per ticket for up to 100 tickets and $17 per ticket thereafter.
The charges for booking 100 tickets will be:
[tex]500 + 20\times 100 = \$2500[/tex]
If you by more than 100 tickets theme park charges $17,
Thus, charges for x tickets will be = [tex]2500+ 17(x - 100)[/tex]
The limit equation represents the average cost per ticket as the number of tickets purchased becomes very high.
The Cost of one ticket of the theme park = [tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}[/tex]
Now solve the above limit equation that will gives you the average cost per ticket as the number of tickets purchased becomes very high.
[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}= \lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}[/tex]
[tex]\lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}=0+17-0[/tex]
Hence, the cost per ticket is $17 as the number of tickets purchased becomes very high.
Answer: [tex]\lim_{n \to \infty} a_n \frac{2500+17(x-100)}{x} =17[/tex]
Step-by-step explanation: I got this correct on Edmentum.
