It is currently Tue Sep 26, 2017 5:43 am

 2 posts • Page 1 of 1
Author Message
x(x-y)
 Post subject: Exponential Decay Question  |  Posted: Sun Oct 02, 2011 1:31 pm

Original Member

Joined: Sat Aug 06, 2011 3:44 pm
Posts: 298
Location: UK

 On a recent maths homework set, I came across a question that I'm having trouble with. It says:"A bath is filled with water at a temperature of 40°C. After t minutes the temperature has fallen to$\displaystyle (10 + 30e^{-0.04t})$°C."a) Find the rate at which the temperature is falling when the temperature is 38°C.So, I had$\displaystyle 10 + 30e^{-0.04t}=38$$\displaystyle \Rightarrow 30e^{-0.04t}=28$$ \displaystyle -1.2t\,ln e = ln 28$So, $\displaystyle t = \frac{ln 28}{-1.2} = -2.7768$The, I differentiated the equation in the question$\displaystyle \dfrac{dT}{dt} = -1.2e^{-0.04t}$to obtain the rate, which I put the time calculated above into to get:$\displaystyle -1.2e^{-0.04(-2.7768)} = -1.341$°C/min.However, the book states that the answer is actually -1.12°C/min. Where have I gone wrong?Thanks in advance! _________________"Nature doesn't care what we call it, she just does it anyway".- Feynman
x(x-y)
 Post subject: Re: Exponential Decay Question  |  Posted: Sun Oct 02, 2011 2:32 pm

Original Member

Joined: Sat Aug 06, 2011 3:44 pm
Posts: 298
Location: UK

 Never mind, I got the answer! I forgot to divide by the 30, rookie mistake! _________________"Nature doesn't care what we call it, she just does it anyway".- Feynman
 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 2 posts • Page 1 of 1

Who is online
 Users browsing this forum: No registered users and 0 guests You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum