Question

A Warming Liquid - A liquid is taken out of a refrigerator and placed in a warmer room, where its temperature, in F, increases over time. It can be modeled using the equation Tm 74 390.87m. (a) What temperature did the liquid start at? Show the work that leads to your answer. (b) What is the temperature of the room?

Answer 1

Answer:

The temperature at the start is 35F

The temperature of the room is 74F

Step-by-step explanation:

Given

$T(m) = 74 - 39(0.87)^m$

Solving (a): The temperature at the start.

To do this, we set: $m = 0$

So, we have:

$T(0) = 74 - 39(0.87)^0$

$T(0) = 74 - 39*1$

$T(0) = 74 - 39$

$T(0) = 35$

Hence, the temperature at the start is 35F

Solving (b): The room temperature

We have:

$T(m) = 74 - 39(0.87)^m$

To get the temperature of the room, we simply remove the exponential function.

So, we have:

$Initial = 74$

Hence, the temperature of the room is 74F