Answer:
The differential equation becomes -
i.e.
Step-by-step explanation:
Given - The rate of change of the volume V of water in a tank with respect to time t is directly proportional to the cubed root of the volume.
To find - Write a differential equation that describes the relationship.
Proof -
Rate of change of volume V with respect to time t is represented by 
Now,
Given that,
The rate of change of the volume V of water in a tank with respect to time t is directly proportional to the cubed root of the volume.
⇒
∝ ![\sqrt[3]{V}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7BV%7D)
Now,
We know that, when we have to remove the Proportionality sign , we just put a constant sign.
Let k be any constant.
So,
The differential equation becomes -
i.e.
3/2x - 3 = y
using y = mx + b, where m is slope and b is the y intercept, we can eliminate the top two answers by finding the y intercept at -3.
You can find the slope of the graph by using any given point and then calculating rise over run. In this case, the rise is 1.5, and the run is 1, which equates to 3/2
b = -3
m = 3/2
Can you please take a picture of the question? I can’t see anything