Question

When a new cellphone is put on the market, the demand each month can be described by the function C of t is equal to negative square root of the quantity t squared plus 4 times t minus 12 end quantity plus 3 where C (t) represents the demand of the cellphone (measured in millions of people) and the time, t, is measured in months. Which of the following solution(s) are valid for a positive demand? (7, 0) and (3, 0) (–6, 3) and (2, 3) (6, 3) (2, 3)

Answer 1

The valid solutions for a positive demand are (7, 0) and (3, 0).

Step-by-step explanation:

To determine the valid solutions for a positive demand, we need to find the values of t that make the demand function C(t) positive. The function C(t) is equal to -√(t^2 + 4t - 12) + 3. To find the valid solutions, we need to find the values of t that make C(t) greater than 0.

1. Substitute C(t) with 0 and solve for t:
0 = -√(t^2 + 4t - 12) + 3
-3 = -√(t^2 + 4t - 12)
9 = t^2 + 4t - 12
t^2 + 4t - 21 = 0

2. Solve the quadratic equation t^2 + 4t - 21 = 0:
(t - 3)(t + 7) = 0
t = 3 or t = -7

Therefore, the valid solutions for a positive demand are (7, 0) and (3, 0).

Answer 2

(2, 3)

Step-by-step explanation: