April 11th, 2017, 08:11 PM  #1 
Member Joined: Feb 2017 From: henderson Posts: 36 Thanks: 0  A bar of metal is cooling from explain! I want to understand on how to do this problem. Please try not to give me the answer thank you! 
April 12th, 2017, 02:21 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,084 Thanks: 699 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
The formula at the end: $\displaystyle H = 23 + 977e^{0.1t}$ describes the temperature, $\displaystyle H$, at any given point in time, $\displaystyle t$. Note that $\displaystyle t$ is in minutes. It is an exponential decay function, so it will rapidly drop with increasing $\displaystyle t$ and then smooth out to a plateau. Try putting in different values of $\displaystyle t$ to calculate $\displaystyle H$ at different times. What value of $\displaystyle t$ do you need to substitute in to calculate $\displaystyle H$ after 1 hour? For the average part, you will need to use the formula for the average. Basically $\displaystyle \bar{x} = \frac{\int_{t_1}^{t_2} f(x) dx}{t_2t_1}$ This is very similar to the concept of "add up the numbers and divide by the number of numbers" except that your function is continuous, not discrete, so instead of adding numbers together, you perform an integral (which is sort of like a continuous sum) and instead of dividing by the number of numbers, you divide by the size of the interval that you want to calculate the average for. Therefore, if you wanted to calculate the average $\displaystyle H$ for the first hour $\displaystyle t_1 = 0$ $\displaystyle t_2 = 60$ $\displaystyle \bar{H} = \frac{\int_{0}^{60} (23 + 977e^{0.1t}) dt}{600}$ Let me know how it goes 

Tags 
bar, cooling, metal 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Newtons law of cooling  junzy  Applied Math  2  April 20th, 2015 11:18 AM 
Lightnut  like a metal nut which bolts go in  Threads are light's wavelength  BenFRayfield  Physics  0  January 13th, 2015 07:45 PM 
newtons law of cooling  ineedhelpnow  Differential Equations  5  July 17th, 2014 02:45 AM 
Cooling down an oven  brownenterprises  Complex Analysis  0  March 5th, 2014 11:41 AM 
How do I find out how much metal the container consists of?  mathismydoom  Algebra  5  October 11th, 2012 04:27 AM 