If the doubling time of a state's population is 42 years, how long does it take for the population to increase by a factor of 16?
doublexdoublexdoublexdouble=16
So would your doublexdoublexdoublexdouble=16
be 2 x 2 x 2 x 2= 16??? I am a liitle confused on why you used double?
To determine how long it takes for the population to increase by a factor of 16, we can use the concept of doubling time.
Since the doubling time is 42 years, it means that the population doubles every 42 years.
To find out how many doubling periods it takes for the population to increase by a factor of 16, we divide the factor of increase (16) by 2 (since the population doubles each time).
16 ÷ 2 = 8
Therefore, it takes 8 doubling periods for the population to increase by a factor of 16.
Since each doubling period is 42 years, we can calculate the total time it takes by multiplying the number of doubling periods by the doubling time:
8 × 42 = 336
Therefore, it takes 336 years for the population to increase by a factor of 16.
To find how long it takes for a population to increase by a factor of 16 when the doubling time is known, you can use logarithms.
Let's break down the problem step by step:
1. Determine the number of doubling periods to increase by a factor of 16:
Since the doubling time is 42 years, the number of doubling periods required to increase the population by a factor of 16 can be calculated as follows:
Doubling periods = log2(16)
= log2(2^4)
= 4
2. Calculate the total time required to complete those doubling periods:
Multiply the number of doubling periods by the doubling time:
Total time = Doubling periods * Doubling time
= 4 * 42
= 168 years
Therefore, it would take approximately 168 years for the population to increase by a factor of 16 when the doubling time is 42 years.