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# Derivatives and Application of the Derivative

F(t) = 10,000 / 10 + 50e ^-0.5t

HOW do I obtain the derivative?
What is the "e" portion of the problem?

I know the derivative = 250,000e^-0.5t/ (10+50e ^-0.5t)^2

Please describe in detail the steps taken to arrive at this answer.
For example, Why is the top of the equation 250,000e^-0.5t?
Why is the bottom (10+50e^-0.5t)^2?
Where does the ^2 on the bottom come from?
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Please describe in detail, when t = 0, 1, 2, 3, 4,...20 for the solution of f(t).

t=0, f(t) = 166.67
t=1, f(t) = 247.98
t=2, f(t) = 352.19

I want to know how to solve the problem on my own, I don't understand How to put in a variable into the equation and arrive at an answer.
Please show me in detail how to solve
f(t) = 10,000 / 10 + 50e ^-0.5t
when t=2.
I don't understand HOW to solve the portion: 10 + 50e^-0.5t
when t =2. I know the answer, HOW does one arrive at it?
Is the 50e^-0.5 the square root of 2 times 50e?
Please describe the process of putting a number at t and working it out.

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