Differentiation of Exponential Functions: v'(10)=37,500^e10/8

SnappleG

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Hello everyone,

Can you please explain how to solve v'(10)=37,500^e10/8?

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

* I figured it out 37,500 * 3.49034~130,888[FONT=MathJax_Main][/FONT][FONT=MathJax_Main][/FONT]
 
Last edited:
Hello everyone,

Can you please explain how to > > > solve < < <v'(10)=37,500^e10/8?

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 step by step 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

You put the "^" in the wrong places, you are missing grouping symbols around exponents,
and you are "evaluating," not "solving."

Here is most of your post with some amendments:

Evaluate 37,500e^(10/8).

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)= 37,500e^(10/8)

Can you please explain step by step how to evaluate v'(10) = 37,500e^(10/8)?

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, now that you know that you should enter your example as "112500e^(4/2)" or just

as "112500e^(2)" in a calculator that shows that kind of display, try that first, and then come

back to this thread to tell us if your display gives a value that will round to 831,269.
 
You put the "^" in the wrong places, you are missing grouping symbols around exponents,
and you are "evaluating," not "solving."

SnappleG, now that you know that you should enter your example as "112500e^(4/2)" or just

as "112500e^(2)" in a calculator that shows that kind of display, try that first, and then come

back to this thread to tell us if your display gives a value that will round to 831,269.

Thank you, I usually use a basic calculator - at least all previous problems I had to solve & evaluate did not need any complex calculations. English is my 2nd language and that is way I misused solve.
 
Thank you, I usually use a basic calculator - at least all previous problems I had to solve & evaluate did not need any complex calculations. English is my 2nd language and that is way I misused solve.
On my calculator, the \(\displaystyle e^x\) function is the inverse of the \(\displaystyle \ln\) function. That is, "<SHIFT>-ln".

Using the built-in Windows calculator set to "Scientific" on its View menu, enter x, then click the "Inv" box and the "ln" key.
 
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