CR Circuit Question (Calculus)

[will.i.am2]

A capacitor and resistor are connected as shown across a 10V d.c. supply. The voltage across the capacitor will increase at an exponential rate given by the equation
v = V - Vet/CR
a) Plot the graph of the capacitor voltage from the equation for values of t between 0 and 24 seconds.
vc = V (1-et/CR) , V = 10v, Capacitor = 100µF, Resistor = 47kΩ
CR = 100µF times 47kΩ = 4.7
done part a. but I need someone to check it for me please?

(b)From the graph determine its gradient at t = 5 seconds.
I have done the graph and after calculating it; it gives me a gradient of -10? I don't know if that's the right answer.

(c) Using calculus determine the gradient of the equation and from this the gradient when t = 5 seconds.
I have attempted it my way and I am not getting the right answer. I have been told by the teacher that the answer should be in minus and both gradient answer should be close.
So, any help would be appreciated.
thanks

 

[Mark44]

A capacitor and resistor are connected as shown across a 10V d.c. supply. The voltage across the capacitor will increase at an exponential rate given by the equation
v = V - Vet/CR
a) Plot the graph of the capacitor voltage from the equation for values of t between 0 and 24 seconds.
vc = V (1-et/CR) , V = 10v, Capacitor = 100µF, Resistor = 47kΩ
CR = 100µF times 47kΩ = 4.7
done part a. but I need someone to check it for me please?(b)From the graph determine its gradient at t = 5 seconds.
I have done the graph and after calculating it; it gives me a gradient of -10? I don't know if that's the right answer.

That's not what you show in the attached image, which is -0.1. Is the slope -10 or -.1? The slope is the vertical rise (or drop) divided by the horizontal run.

(c) Using calculus determine the gradient of the equation and from this the gradient when t = 5 seconds.
I have attempted it my way and I am not getting the right answer.

Your derivative is incorrect. You are not using the chain rule correctly.

Also, be consistent with the letters you use. You are using both V and v, which is confusing, since these could represent different quantities.

I have been told by the teacher that the answer should be in minus and both gradient answer should be close.
So, any help would be appreciated.
thanks

One more thing: since this is a calculus problem, it should NOT be posted in the Precalculus section. I am moving it to the Calculus & Beyond section.