My Math Forum Differentiation of Exponential Functions: 37,500^e10/8

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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=2008-1998=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:  Originally Posted by SnappleG 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=2008-1998=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
I don't understand what this has to do with the previous problem.

Quote:
 The answer is ~ 831,269 I just don't understand how you come to ~ 831,269
You don't.
10/8= 5/4= 1.24. $$e^{1.25}= 3.4903429$$
37500 times 3.4903429 is 130,889, not 831,269.

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