SOLUTION: The length l(T)of a bar depends on the temperature T, according to the law l(T)=l_o*e^(∝T), where l_o is the length of the bar when T=0 and ∝ is a positive constant.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The length l(T)of a bar depends on the temperature T, according to the law l(T)=l_o*e^(∝T), where l_o is the length of the bar when T=0 and ∝ is a positive constant.       Log On


   

Question 736229: The length l(T)of a bar depends on the temperature T, according to the law
l(T)=l_o*e^(∝T), where l_o is the length of the bar when T=0 and ∝ is a positive constant. Calculate the percentage change in length when T increases from T=10 to T=80 and ∝=0.001
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
l%28t%29=l%5B0%5D%2Ae%5E%28alpha%2AT%29 and with alpha=0.001 l%28t%29=l%5B0%5D%2Ae%5E%280.001T%29

When T=10 l%2810%29=l%5B0%5D%2Ae%5E%280.001%2A10%29=l%5B0%5D%2Ae%5E0.01

When T=80 l%2880%29=l%5B0%5D%2Ae%5E%280.001%2A80%29=l%5B0%5D%2Ae%5E0.08



The relative increase, as a fraction of the size at t=10 is
%28l%2880%29-l%2810%29%29%2Fl%2810%29=l%2880%29%2Fl%2810%29-1=e%5E0.07-1= approx. 1.0725-1=0.0725
That is 0.0725%2F1=7.25%2F100=7.25%