Derivative of Exponential Function (average typing speed N)

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AGlas9837

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Jan 23, 2008
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I have an answer to the following word problem but don't think my derivative is correct. The average typing speed N (in words per minute) after t weeks of lessons is modeled by:

N=95/1+8.5e^-0.12t

For the derivative, I get N'=(1+8.5e^-.12t)(0)-95(8.5e^-.126)(-.12)/(1+8.5e^-0.12t)^2 which gives:
11.4(8.5e^-.12t/(1+8.5e^-.12t)^2

The rates at which the typing speed is changing are to be calculated at 5, 10 and 30 weeks. When I plug these numbers into my derivative, I'm getting 14.9, 16.5 and 2.63 wpm which doesn't make sense.
 
AGlas9837 said:
I have an answer to the following word problem but don't think my derivative is correct. The average typing speed N (in words per minute) after t weeks of lessons is modeled by: N=95/1+8.5e^-0.12t
Click to expand...
What you have posted means the following:

. . . . .\(\displaystyle N\, =\, \frac{95}{1}\, +\, 8.5e^{-0.12}t\)

...or:

. . . . .\(\displaystyle N\, =\, \frac{95}{1}\, +\, 8.5e^{-0.12t}\)

At a guess, you may have actually meant the following:

. . . . .\(\displaystyle N\, =\, \frac{95}{1\, +\, 8.5e^{-0.12t}}\)

Please reply with confirmation or correction. Thank you! :D

Eliz.
 
Now - please clean up your answer - using proper parentheses - if you really want us to help you.
 
AGlas9837 said:
Is this any plainer??

More plainer

N' = 11.4 * 8.5 * e^-(.12t) /[ 1 + 8.5 * e^-(.12 * t)]^2

= 96.9 * e^-(.12t)/[ 1 + 8.5 * e^-(.12 * t)]^2
Click to expand...

Now tell me why doesn't your answer make sense to you!!
 
I see how you got that now. I had left the 8.5e^-.12 separated from 95 and -.12. Either way, it comes out the same. What I wasn't sure about in the beginning was the derivative of (1+8.5e^-.12t) which I see now is (8.5e^.12)(-.12).
 
AGlas9837 said:
The rates at which the typing speed is changing are to be calculated at 5, 10 and 30 weeks. When I plug these numbers into my derivative, I'm getting 14.9, 16.5 and 2.63 wpm which doesn't make sense.
Click to expand...

My question was:

Why didn't your answer make sense to you?
 
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