The world population in 1992 is 5.42 billion. If its population doubled every
41 years, what would its population be in 41 years?
41 years, what would its population be in 82 years?
82 years, what would its population be in 164 years?
To find the population in each given time frame, we'll use the formula for exponential growth:
P = P0 * (1 + r)^t
Where:
P = population after time t
P0 = initial population
r = growth rate (doubling time)
t = time in years
Given:
P0 = 5.42 billion
r = 41 years
1. Population in 41 years:
P_41 = 5.42 billion * (1 + 1)^1 = 5.42 billion * 2 = 10.84 billion
2. Population in 82 years:
P_82 = 5.42 billion * (1 + 1)^2 = 5.42 billion * 4 = 21.68 billion
3. Population in 164 years:
P_164 = 5.42 billion * (1 + 1)^4 = 5.42 billion * 16 = 86.72 billion
To find the population after a certain number of years, we can use the formula for exponential growth: P(t) = P(0) * (2^(t/n)), where P(t) is the population after t years, P(0) is the initial population, and n is the number of years it takes for the population to double.
1. For 41 years:
Given that the initial population (P(0)) in 1992 is 5.42 billion, and the population doubles every 41 years, we can plug these values into the formula:
P(41) = 5.42 billion * (2^(41/41))
P(41) = 5.42 billion * (2^1)
P(41) = 5.42 billion * 2
P(41) = 10.84 billion
So, the population in 41 years would be approximately 10.84 billion.
2. For 82 years:
To find the population after 82 years, we need to double the population twice:
P(82) = 5.42 billion * (2^(82/41))
P(82) = 5.42 billion * (2^2)
P(82) = 5.42 billion * 4
P(82) = 21.68 billion
So, the population in 82 years would be approximately 21.68 billion.
3. For 164 years:
To find the population after 164 years, we need to double the population four times (doubling the population every 41 years for a total of 4 intervals):
P(164) = 5.42 billion * (2^(164/41))
P(164) = 5.42 billion * (2^4)
P(164) = 5.42 billion * 16
P(164) = 86.72 billion
So, the population in 164 years would be approximately 86.72 billion.
well, I'd say 4.42*2 billion
then, in 82 = 41+41, 4.42*4
then, in 164 = 82+82, 4.42*4