Can you please check my work

Can you please tell me where I went wrong becasue my teacher said that answer is 13720

2. Originally Posted by supersaiyan
Can you please check my work

Can you please tell me where I went wrong becasue my teacher said that answer is 13720
Let me get this straight.

You have a function $f(x) = 400e^{\frac{\ln(2.375)}{2}x}$...

And you have to find out what $f'(10)$ is?

3. Originally Posted by supersaiyan
Can you please check my work

Can you please tell me where I went wrong becasue my teacher said that answer is 13720

4. Yes, i have, he said check your work again

5. Originally Posted by Mush
Let me get this straight.

You have a function $f(x) = 400e^{\frac{\ln(2.375)}{2}x}$...

And you have to find out what $f'(10)$ is?
Yes

6. Originally Posted by supersaiyan
Can you please check my work

Can you please tell me where I went wrong becasue my teacher said that answer is 13720
$f(x) = 400 e^{kx}$ where $k = \frac{1}{2} \ln (2.375)$.

$f'(x) = 400 k e^{kx}$.

$f'(10) = 400 k e^{10k}$.

$10 k = 5 \ln (2.375) = \ln (2.375)^5 \Rightarrow e^{10k} = 2.375^5$.

So $f'(10) = 200 [\ln (2.375)] \, 2.375^5$.

Now use a calculator if a decimal approximation is required.