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November 1st, 2013, 07:11 PM   #1
 
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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
SnappleG is offline  
 
November 1st, 2013, 08:56 PM   #2
 
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Re: Differentiation of Exponential Functions: 37,500^e10/8

* I figured it out 37,500 * 3.49034~130,888
SnappleG is offline  
November 2nd, 2013, 07:50 AM   #3
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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. [tex]e^{1.25}= 3.4903429[/tex]
37500 times 3.4903429 is 130,889, not 831,269.
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