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

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

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 2. Originally Posted by SnappleG 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

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)

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.

3. Originally Posted by lookagain
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.

4. Originally Posted by SnappleG
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 $e^x$ function is the inverse of the $\ln$ 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.