The temperature is changing at a certain rate. What is the temperature when t=5?

In summary, the question asks for the temperature of a pizza that has been heated to 350 degrees Fahrenheit and then placed in a 75°F room at time t=0 minutes. The rate of change of the pizza's temperature is -110e-0.4t degrees Fahrenheit per minute. Using the formula T= ∫(dT/dt) dt, we can find the temperature of the pizza at time t=5 minutes, which is approximately 112°F. This problem is related to Newton's Law of Cooling.
  • #1
lude1
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0

Homework Statement



A pizza, heated to a temperature of 350 degrees Fahrenheit, is taken out of an oven and placed in a 75°F room at time t=0 minutes. The temperature of the pizza is changed at a rate of -110e-0.4t degrees Fahrenheit per minute. TO the nearest degree, what is the temperature of the pizza at time t=5 minutes?

Answer: 112°F

Homework Equations



f'(t) = -ky?
All I can think of is that this problem is related to Newton's Law of Cooling.

The Attempt at a Solution



The rate of change or derivative is -110e-0.4t. I think what you're suppose to do is find how much the temperature dropped and subtract this number to the original temperature, 350°. I originally thought, if I plugged in t=5 into
-110e-0.4t and subtract this number from 350°, then I would have my answer. But, of course, this is wrong.
 
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  • #2
lude1 said:
The rate of change or derivative is -110e-0.4t

So we have this meaning that

dT/dt = -110e-0.4t ⇒ T= ∫(dT/dt) dt

So what is T equal to?
 

FAQ: The temperature is changing at a certain rate. What is the temperature when t=5?

1. How do you calculate the temperature at a specific time?

The temperature at a specific time can be calculated by using the formula T = T0 + rt, where T represents the temperature at the specific time, T0 is the initial temperature, r is the rate of change, and t is the time elapsed.

2. What is the significance of the rate of change in temperature?

The rate of change in temperature indicates how quickly the temperature is increasing or decreasing. It is an important factor in understanding the trend of temperature change and can help predict future temperature patterns.

3. Can the temperature at a specific time be accurately predicted?

It is difficult to accurately predict the exact temperature at a specific time due to various factors such as climate variability and natural events. However, by analyzing past data and considering current trends, it is possible to make an estimation of the temperature at a specific time.

4. How does the temperature change rate vary in different regions?

The temperature change rate can vary significantly in different regions due to various factors such as geographical location, altitude, and climate patterns. For example, regions near the equator may experience a faster temperature change rate compared to regions near the poles.

5. Can the temperature change rate be affected by human activities?

Yes, human activities such as greenhouse gas emissions and deforestation can contribute to an increase in the temperature change rate. This can lead to more extreme weather events and changes in climate patterns.

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