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.

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%

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eudora eudora · Answer 2 · 2019-10-06T03:51:57+02:00

Answer:

Sales will decrease by 10.35%

Step-by-step explanation:

Number of collars sold each year is represented by the function

x³ + 200p² = 17500

Where x = Number of collars in thousands

p = price of a collar

Since price of the collar is increased by $2, therefore each collar will cost = $6

Now from the given equation,

x³ + 200(6)² = 17500

x³ = 17500 - 7200

x³ = 10300

x = 21.758

Since the value of x is in thousands so number of collars sold will be = 21758

Earlier number of collars selling = 24272.

Decrease in sales = 24272 - 21758 = 2514

Percentage drop in sales = [tex]\frac{\text{Decrease in sales}}{\text{Number of collars selling earlier}}\times 100[/tex]

= [tex]\frac{2514}{24272}\times 100=10.4[/tex]%

Sales will decrease by 10.35%