Question

The temperature T(⁰F) of a room at time t minutes is given by the formula below.

T = 85 - 12 √25 - t for 0 ≤ t ≤ 25
Find the room's temperature when t = 0, t = 16, and t = 25.

Answer 1

The temperature of the room at different times can be calculated using the formula T = 85 - 12 √(25 - t) for 0 ≤ t ≤ 25. When t = 0, the temperature is 25°F. When t = 16, the temperature is 49°F. When t = 25, the temperature is 85°F.

Step-by-step explanation:

The formula given to calculate the temperature T(⁰F) of a room at time t minutes is: T = 85 - 12 √(25 - t) for 0 ≤ t ≤ 25. To find the room's temperature when t = 0, t = 16, and t = 25, we substitute the values of t into the formula and solve for T.

When t = 0: T = 85 - 12 √(25 - 0) = 85 - 12 √25 = 85 - 12 * 5 = 85 - 60 = 25°F.

When t = 16: T = 85 - 12 √(25 - 16) = 85 - 12 √9 = 85 - 12 * 3 = 85 - 36 = 49°F.

When t = 25: T = 85 - 12 √(25 - 25) = 85 - 12 √0 = 85 - 12 * 0 = 85 - 0 = 85°F.