7r=-7/2
divide both sides by 7 to get r by itself
(7r)/(7) = (-7/2)/(7)
if you don't quite see it, think of multiplying both sides by 1/7 instead (its the same thing as dividing by 7)
(7r)*(1/7)=(-7/2)*(1/7)
r=-1/2
Solution:
Given :
.............(1)
where, B = aP = birth rate
D =
= death rate
Now initial population at t = 0, we have
= 220 ,
= 9 ,
= 15
Now equation (1) can be written as :

.................(2)
Now this equation is similar to the logistic differential equation which is ,

where M = limiting population / carrying capacity
This gives us M = a/b
Now we can find the value of a and b at t=0 and substitute for M
and 
So, 
= 
= 132
Now from equation (2), we get the constants
k = b = 
= 
The population P(t) from logistic equation is calculated by :



As per question, P(t) = 110% of M



Now taking natural logs on both the sides we get
t = 36.216
Number of months = 36.216
Those are all the answers hope this helps.
X=number of girls.
y=number of boys.
We can suggest this system of equations:
2/7 x=3/5 y ⇒10x=21y ⇒x=21/10 y
y=x-165
We can solve this problem by substitution method:
x=(21/10)(x-165)
10x=21x-3465
10x-21x=-3465
-11x=-3465
x=-3465 /-11=315
y=x-165=315-165=150
Number of children=number of girls + number of boys
Number of children=315 +150=465
Answer: there were 465 children at the festival.