Answer:
14.2 years
Step-by-step explanation:
The multiplier of the population each year is 1 +5% = 1.05, so after n years the population has been multiplied by 1.05^n. You want to find the value of n that makes this expression equal to 2:
2 = 1.05^n
log(2) = n·log(1.05) . . . . . take logarithms
log(2)/log(1.05) = n ≈ 14.2
Growing at a rate of 5% per year, it will take about 14.2 years for the population to double.
Carol would have sold 60 magazine subscriptions while Jennifer had sold 30 magazine subscriptions
We can either use the quadratic formula or completing the square.
I'll use the method if completing the square.
x^2 + 10x + 12 = 36
Move the constant over to the other side.
x^2 + 10x = 24
Add (b/2)^2 to both sides.
x^2 + 10x + (10/2)^2 = 24 + (10/2)^2
x^2 + 10x + 5^2 = 24 + 5^2
x^2 + 10x + 25 = 24 + 25
Factor the left side and add the terms on the right side
(x+5)(x+5) = 49
(x+5)^2 = 49
Find the square root of both sides.
x + 5 = +/- 7
Move 5 over to the other side by subtracting it.
x = -5 + -7 = -12
OR
x = -5 - (-7) = 2
So x = -12 or x = 2.