The world population in the year 2018 was approximately 7.6 billions and it grows at the rate 1.1% per year. Assuming that the rate does not change over the next years:
a) Write a formula for the world population size depending on time
b) What would be the world population in 2025?
c) In what year the world population will double? (Round your answers to the nearest tenth)
P (year - 2018) = 7.6*10^9 * 1.011^(year - 2018)
a) The formula for the world population size depending on time can be written as:
P(t) = P(0) * (1 + r)^t
Where:
P(t) represents the population at time t
P(0) represents the initial population (7.6 billion in 2018)
r represents the growth rate (1.1% per year)
t represents the number of years
b) To calculate the world population in 2025, we need to substitute the values into the formula:
P(2025) = P(0) * (1 + r)^(2025-2018)
P(2025) = 7.6 billion * (1 + 0.011)^7
P(2025) = 7.6 billion * (1.011)^7
Using a calculator, P(2025) is approximately 8.78 billion.
c) To calculate the year in which the world population will double, we can set up the equation:
2 * P(0) = P(0) * (1 + r)^t
Dividing both sides by P(0), we get:
2 = (1 + r)^t
Taking the logarithm of both sides to solve for t:
log(2) = t * log(1 + r)
t = log(2) / log(1 + r)
Substituting the value of r (0.011) into the equation:
t = log(2) / log(1.011)
Using a calculator, t is approximately 62.7 years.
Thus, the world population will double in approximately 62.7 years, which rounds to the nearest tenth to the year 2080.
a) To calculate the world population size depending on time, we can use the formula for exponential growth:
P(t) = P(0) * (1 + r)^t
Where:
P(t) is the population at time t
P(0) is the initial population (in this case, 7.6 billion)
r is the annual growth rate (in this case, 1.1% or 0.011)
t is the number of years
b) To find the world population in 2025, we substitute the values into the formula:
P(2025) = 7.6 * (1 + 0.011)^(2025-2018)
Simplifying:
P(2025) = 7.6 * (1.011)^7
Using a calculator, we find:
P(2025) ≈ 8.7 billion
So, the estimated world population in 2025 would be approximately 8.7 billion.
c) To find the year when the world population will double, we can set up the equation:
2P(0) = P(0) * (1 + r)^t
Dividing both sides by P(0):
2 = (1 + r)^t
Taking the logarithm of both sides to solve for t:
log(2) = t * log(1 + r)
Solving for t:
t = log(2) / log(1 + r)
Using the given growth rate:
t ≈ log(2) / log(1.011)
Using a calculator, we find:
t ≈ 63.6 years
So, the world population is expected to double in approximately 63.6 years. We can round this to the nearest tenth:
t ≈ 63.6 years.
It's important to note that this is an estimated calculation based on a constant growth rate and does not take into account other factors that may influence population growth.