The number x (in thousands) of cat flea collars demanded each year when the price of a collar is p dollars is expressed by the function x^3+200p^2=17,500. The collars are currently selling for $4 each and the annual number of sales is 24,272. Find the approximate decrease in sales of the collar if the price of each collar is raised by $2.

Question

Mathematics

Athena

27 February, 22:37

The number x (in thousands) of cat flea collars demanded each year when the price of a collar is p dollars is expressed by the function x^3+200p^2=17,500. The collars are currently selling for $4 each and the annual number of sales is 24,272. Find the approximate decrease in sales of the collar if the price of each collar is raised by $2.

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Adrien Michael · Answer 1

Actually If you ignore the initial x until the end it all makes sense. So we are given x^3+200p^2=17500. p becomes $6, plug that in and you get x^3=10300, take the cube root of that and you get 21.758 (in thousands) so multiply by 1000 and you get 21,758. The initial x is 24,272, find the percentage and you get 89.6%, we want the decrease so the percentage decrease is 10.4%