Answer
Input= 5
Output= 120
Step-by-step explanation:
The input goes up by 1, so m=5
The output shows how many hours there are in that many days so blank=120
Answer:
magnitude is always postive
so, it will be +2.5 , so C
Answer:
See Below.
Step-by-step explanation:
We are given that:

Where <em>I₀</em> and <em>k</em> are constants.
And we want to prove that:

From the original equation, take the derivative of both sides with respect to <em>t</em>. Hence:
![\displaystyle \frac{d}{dt}\left[I\right] = \frac{d}{dt}\left[I_0e^{-kt}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5BI%5Cright%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5BI_0e%5E%7B-kt%7D%5Cright%5D)
Differentiate. Since <em>I₀ </em>is a constant:
![\displaystyle \frac{dI}{dt} = I_0\left(\frac{d}{dt}\left[ e^{-kt}\right]\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdI%7D%7Bdt%7D%20%3D%20I_0%5Cleft%28%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5B%20e%5E%7B-kt%7D%5Cright%5D%5Cright%29)
Using the chain rule:

We have:

Substitute:

Distribute and simplify:

Hence proven.
The answer is C. Try 18=k/4. 18*4=72. Take 72/24=3.