Question

When an object is removed from a furnace and placed in an environment with a constant temperature of 70°F, its core temperature is 1500°F. One hour after it is removed, the core temperature is 1170°F. (a) Write an equation for the core temperature y of the object t hours after it is removed from the furnace. (Round your coefficients to four decimal places.)

Answer 1

The equation for the core temperature y of the object t hours after it is removed from the furnace can be written as y = 1500 * (70/1500)ˣ.

Step-by-step explanation:

The equation for the core temperature y of the object t hours after it is removed from the furnace can be written as:

y = 1500 * (70/1500)ˣ

Let's break down the equation step by step:

1. The initial core temperature is 1500°F
2. The constant temperature of the environment is 70°F
3. We use the formula for exponential decay: y = A * (B/A)ˣ
4. A is the initial temperature, B is the final temperature, and t is the time in hours
5. For this problem, B is the constant temperature of the environment
6. Plug in the values to get the equation: y = 1500 * (70/1500)ˣ