Question

1) Katie's Boat Rental has a marginal profit function of ??(?) = 20? − 50. Yesterday Katie made a profit of $400 on 10 boat rentals. What is the profit function, ?(?), for Katie's Boat Rental?

2) John's truck Repair has a channel of repair videos. The total number of subscribers per week is represented by the function ?(?) = 60√? , where t is weeks after he started the channel.

What is the average number of subscribers on his channel between weeks 4 and 9 after starting the channel?

Answer 1

The marginal profit is: M. P(x) = 200-50 Now, the total profit is given as: P(x) = rex dx +C P(x) = f (20x-50) dx +C P(x) = 20 x² - 5ox +C Now, P(x) = 10x² - 50 x +C When x=10 Plio) = $400. 10(10)2 - Sol10)+c = 400 - 1000 - 500 + c = 400 ² 500 + c = 400 [c=-100 P(x) = [10x² - 5ox - 100 / Ano : per week are: (2) Total no. of subscribers s(t) = GOVE Now, the average no of are : subscribers b/w weeks 4 and wech a 312/ Sang = 144 S bore at = so I that Sarg. = 12 (122) a = 12 x 2 ( 1972 _ (4) 3/2) Saug. = 8 ( (32 32 _ (2²) 32) Say. = 8 ( 33 - 23) - 8(27-8) Sang. = 8819 = (152 cm