Question

A chemistry student mixes two solutions to study the properties of the resulting mixture. The temperature of the new solution is given by the function

T = 24t − 2t2 + 5, where T is the temperature in degrees Celsius and t is the time elapsed in seconds after the solutions are mixed. What is the time interval that the temperature of the solution will be at least 69°C?


[2, 6]


[3, 8]


[5, 8]


[4, 8]

Answer 1

[4, 8]

Explanation:

You want to find t such that ...

T ≥ 69

24t − 2t^2 + 5 ≥ 69

t^2 -12t +32 ≤ 0 . . . . . subtract the left side, divide by 2

(t -4)(t -8) ≤ 0 . . . . . . . factor

The factors will have different signs, so their product will be negative, for values of t between 4 and 8. Of course, the equality holds at t=4 and t=8, so the solution interval is ...

t ∈ [4, 8]