I am currently doing a question in which the equation is dN1/dt= -N1 + 0.1N1*N2
However, I am able to follow until the step of -N1(1 - 0.1N2)
after that I'm not able to follow to the step of (-1)N1 (1-N2/10)
Can someone please explain to me how we went from the second step to the third step. That is the only part that has me confused.
-N1(1 - 0.1N2) Hmmmm.
-N1 is the same as -1*N1 or -1(N1)
-.1 is the same as 1/10
-1(N1)(1-N2/10)
Sure! Let me explain how we went from the equation -N1(1 - 0.1N2) to (-1)N1(1-N2/10).
To simplify the expression -N1(1 - 0.1N2), we can distribute the -N1 term into the brackets:
-N1(1 - 0.1N2) = -N1 + (0.1N1N2)
Next, let's rearrange the second term so that it matches the format (-1)N1(1-N2/10):
0.1N1N2 = (N1/10)N2
Now, we can rewrite this as (-1)N1(1-N2/10):
-N1 + (N1/10)N2 = -1*N1 + [(N1/10)N2] = (-1)N1(1-N2/10)
So, in the third step, we essentially rearranged the term (0.1N1N2) as (N1/10)N2 and then combined it with -N1 to match the format (-1)N1(1-N2/10).
I hope this clarifies the process for you! Let me know if you have any further questions.