Understanding the Temperature Function

Oct 13, 2025 by thesweetdesigns.com 18 views

Introduction

When a deli sandwich is placed inside a cooler, its temperature decreases over time. The temperature of the sandwich in degrees Celsius is given by the function $C(t) = 19(0.94)^t$ , where $t$ represents the time in hours. In this article, we will explore the initial temperature of the sandwich and how it cools down over time.

The Initial Temperature

To find the initial temperature of the sandwich, we need to evaluate the function $C(t)$ at $t = 0$ . This is because the initial temperature is the temperature of the sandwich at the beginning, when $t = 0$ .

C(0) = 19(0.94)^0

Since any number raised to the power of 0 is equal to 1, we can simplify the expression as follows:

C(0) = 19(1)

Therefore, the initial temperature of the sandwich is:

19°C

This means that the sandwich was initially at a temperature of 19°C.

Understanding the Temperature Function

The temperature function $C(t) = 19(0.94)^t$ can be broken down into two parts: the initial temperature and the cooling factor. The initial temperature is 19°C, which we have already found. The cooling factor is represented by the number 0.94, which is raised to the power of $t$ .

The cooling factor, 0.94, represents the rate at which the sandwich cools down. Since it is less than 1, the sandwich cools down over time. The higher the value of $t$ , the lower the temperature of the sandwich.

How the Sandwich Cools Down

To understand how the sandwich cools down, we need to evaluate the function $C(t)$ at different values of $t$ . Let's consider the following values of $t$ :

$t = 1$ : $C(1) = 19(0.94)^1 = 17.86°C$
$t = 2$ : $C(2) = 19(0.94)^2 = 16.83°C$
$t = 3$ : $C(3) = 19(0.94)^3 = 15.83°C$

As we can see, the temperature of the sandwich decreases over time. After 1 hour, the temperature drops to 17.86°C. After 2 hours, the temperature drops to 16.83°C. After 3 hours, the temperature drops to 15.83°C.

Conclusion

In conclusion, the initial temperature of the deli sandwich is 19°C. The temperature function $C(t) = 19(0.94)^t$ represents the cooling of the sandwich over time. The cooling factor, 0.94, represents the rate at which the sandwich cools down. By evaluating the function at different values of $t$ , we can understand how the sandwich cools down over time.

References

[1] "Temperature and Cooling". Wikipedia. Retrieved 2023-02-20.
[2] "Exponential Functions". Khan Academy. Retrieved 2023-02-20.

Q&A: A Deli Sandwich Cooling Down

Q: What is the initial temperature of the deli sandwich?

A: The initial temperature of the deli sandwich is 19°C.

Q: How does the temperature function C(t) = 19(0.94)^t represent the cooling of the sandwich?

A: The temperature function C(t) = 19(0.94)^t represents the cooling of the sandwich by using an exponential function. The initial temperature of 19°C is multiplied by the cooling factor 0.94, which is raised to the power of t. This represents the rate at which the sandwich cools down over time.

Q: What is the cooling factor in the temperature function C(t) = 19(0.94)^t?

A: The cooling factor in the temperature function C(t) = 19(0.94)^t is 0.94. This represents the rate at which the sandwich cools down over time.

Q: How does the value of t affect the temperature of the sandwich?

A: The value of t affects the temperature of the sandwich by changing the rate at which the sandwich cools down. As t increases, the temperature of the sandwich decreases.

Q: What happens to the temperature of the sandwich after 1 hour?

A: After 1 hour, the temperature of the sandwich drops to 17.86°C.

Q: What happens to the temperature of the sandwich after 2 hours?

A: After 2 hours, the temperature of the sandwich drops to 16.83°C.

Q: What happens to the temperature of the sandwich after 3 hours?

A: After 3 hours, the temperature of the sandwich drops to 15.83°C.

Q: How can we use the temperature function C(t) = 19(0.94)^t to predict the temperature of the sandwich at any given time?

A: We can use the temperature function C(t) = 19(0.94)^t to predict the temperature of the sandwich at any given time by plugging in the value of t into the function. For example, if we want to know the temperature of the sandwich after 4 hours, we would plug in t = 4 into the function.

Q: What are some real-world applications of the temperature function C(t) = 19(0.94)^t?

A: Some real-world applications of the temperature function C(t) = 19(0.94)^t include:

Predicting the temperature of perishable goods in storage
Understanding the cooling process of food in a refrigerator
Developing temperature control systems for industrial applications

Q: Can we use the temperature function C(t) = 19(0.94)^t to model the cooling of other objects?

A: Yes, we can use the temperature function C(t) = 19(0.94)^t to model the cooling of other objects, as long as the cooling process is exponential in nature.

Conclusion

In conclusion, the temperature function C(t) = 19(0.94)^t represents the cooling of a deli sandwich over time. By understanding the initial temperature, the cooling factor, and the value of t, we can predict the temperature of the sandwich at any given time. The temperature function has real-world applications in predicting the temperature of perishable goods, understanding the cooling process of food, and developing temperature control systems for industrial applications.