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November 1st, 2013, 07:11 PM  #1 
Joined: Nov 2013 Posts: 2 Thanks: 0  Differentiation of Exponential Functions: 37,500^e10/8
Hello Everyone, A tapestry purchased in 1998 for $300,000 is estimated to be worth v(t)=300,000e^t/8 dollars after t years. At what rate will the tapestry be appreciating in 2008? I start v'(t)=300,000e^t/8*1/8=37,500e^t/8 t=20081998=10 v'(10)=37,500^e10/8 Can you please explain how to solve v'(10)=37,500^e10/8? Thank you! I have an example: v'(4)=112,500e^4/2 The answer is ~ 831,269 I just don't understand how you come to ~ 831,269 
November 1st, 2013, 08:56 PM  #2 
Joined: Nov 2013 Posts: 2 Thanks: 0  Re: Differentiation of Exponential Functions: 37,500^e10/8
* I figured it out 37,500 * 3.49034~130,888

November 2nd, 2013, 07:50 AM  #3  
Senior Member Joined: Sep 2007 Posts: 2,409 Thanks: 5  Re: Differentiation of Exponential Functions: 37,500^e10/8 Quote:
Quote:
10/8= 5/4= 1.24. [tex]e^{1.25}= 3.4903429[/tex] 37500 times 3.4903429 is 130,889, not 831,269.  

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500e10 or 8, differentiation, exponential, functions 
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