suppose a population has a doubling time of 15 years. By what factor will it grow in 30 years?
To determine the growth factor of a population with a doubling time of 15 years, we can use the formula:
Growth factor = 2^(time / doubling time)
Given that the doubling time is 15 years and the time period is 30 years, let's substitute these values into the formula:
Growth factor = 2^(30 / 15)
Simplifying this expression, we find that:
Growth factor = 2^2
Calculating 2^2, we get:
Growth factor = 4
Therefore, the population will grow by a factor of 4 in 30 years.
To determine the factor by which a population will grow in a given time period, we can use the concept of doubling time. Doubling time represents the time it takes for a population to double in size.
In this case, we are given that the population's doubling time is 15 years. This means that the population will double in size every 15 years.
To calculate the factor by which the population will grow in 30 years, we need to determine how many doubling periods occur within this time frame.
Since the doubling time is 15 years, we divide the given time period (30 years) by the doubling time:
30 years / 15 years = 2 doubling periods
So, within 30 years, the population will double twice.
Now, let's calculate the factor by which the population will grow. Since the population doubles with each doubling period, we can express it as 2^2, where 2 represents the number of doubling periods.
2^2 = 4
Hence, the population will grow by a factor of 4 in 30 years.