Question

When a new cellphone is put on the market, the demand each month can be described by the function c(t) = -√(t² + 2t - 15) + 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?

1) (5, 3)
2) (3, 3)
3) (6, 0)
4) (4, 0)
5) (-5, 3)
6) (3, 3)

Answer 1

Upon analyzing the function, solutions (5, 3) and (3, 3) are valid for positive demand, whereas (4, 0) represents zero demand, and (6, 0) and (-5, 3) are invalid for positive demand.

Step-by-step explanation:

The solution to the question of demand for the new cellphone using the function c(t) = -√(t² + 2t - 15) + 3 requires finding the time values, t, that result in a positive demand. We first need to ensure that the expression under the square root is non-negative because the square root of a negative number is not real. We then check if the demand, c(t), is positive.

The pairs provided can be substituted into the function to check their validity. Valid solutions are those for which c(t) is positive. Solutions (5, 3) and (3, 3) result in a positive value of c(t), whereas (4, 0) is just at the point of zero demand, so it could be seen as the threshold for positive demand. Solutions (6, 0) and (-5, 3) do not produce a positive demand when substituted into the function.