State the growth factor in each of the following situations.
Canada's population is increasing by 1% per year.
How do I calculate this?
I think Im supposed to use this formula, but I don't know where to plug in what.
tn = ar^n-1
the growth factor = 1.01
so suppose population is 30 million
then in 4 years ...
Population = 30 000 000(1.01)^4
= 30000000(1.04060401)= .....
To calculate the growth factor in this scenario, you can use the formula for exponential growth:
Growth Factor (r) = (New Value / Initial Value)^(1 / Number of Periods) - 1
In this case, let's calculate the growth factor for Canada's population increase of 1% per year.
Step 1: Define the variables:
- Initial Value (a): Current population
- New Value (tn): Population after one year
- Number of Periods (n): Number of years
Step 2: Plug in the values into the formula:
Canada's population increased by 1%, which means the New Value is the Initial Value plus 1% of the Initial Value:
tn = a + (1% * a) = a + 0.01a = 1.01a
Now, substitute tn and a into the formula:
r = (1.01a / a)^(1 / n) - 1
Step 3: Simplify the equation:
The "a" cancels out:
r = 1.01^(1 / n) - 1
So, the growth factor (r) for Canada's population increase of 1% per year is 1.01^(1 / n) - 1, where "n" represents the number of years.