If a population grows at 8% per year, how long will it take the population to double?
it will take n years, where
1.08^n = 2
1.85
Since 2012 the population of Smallville has grown by 8% per year. What is the growth rate?
To calculate the time it takes for a population to double, we need to use the formula for exponential growth:
N = P * (1 + r)^t
Where:
N = Final population size
P = Initial population size
r = Growth rate per time period
t = Number of time periods
In this case, the growth rate is 8% per year, which can be written as 0.08 (since 8% = 8/100 = 0.08), and we want to find out how long it takes for the population to double, so the final population (N) will be 2 times the initial population (P).
Plugging in these values into the formula, we get:
2P = P * (1 + 0.08)^t
Now, we can cancel out the P on both sides of the equation:
2 = (1 + 0.08)^t
Next, we solve for t by taking the natural logarithm (ln) of both sides of the equation:
ln(2) = ln((1 + 0.08)^t)
Using the property of logarithms that states ln(a^b) = b * ln(a), we can simplify further:
ln(2) = t * ln(1.08)
Finally, we solve for t by dividing both sides of the equation by ln(1.08):
t = ln(2) / ln(1.08)
Using a calculator, we can evaluate this expression to find the value of t, which is approximately 9.006.
Therefore, it will take approximately 9.006 years for the population to double.