The population of the world in 1987 was 5 billion and the annual growth rate was
estimated at 2 percent per year. Assuming that the world population follows an
exponential growth model, find the projected world population in 2015.
Assume formula
Population in billions at time t (counting from 1987) as
P(t)=Ae^(kt)
where A and k are constants.
At t=0 (1987),
P(0)=Ae^(0)=A=5
the formula becomes:
P(t)=5e^(kt)
P(1)=5*1.02=5e^(kt) [t=1]
=>
e^(k)=1.02 [t=1]
Take log both sides
k=log(1.02) [natural log]
So
P(t)=5e^(t*log(1.02))
where log(1.02)=0.0198 approx.
To find the projected world population in 2015, we need to use the exponential growth formula:
P(t) = P0 * (1 + r)^t
where:
P(t) represents the population at time t
P0 represents the initial population
r represents the growth rate
t represents the time in years
Given that the population in 1987 (P0) was 5 billion and the annual growth rate (r) was 2 percent, we can substitute these values into the formula:
P(2015) = 5 billion * (1 + 0.02)^(2015-1987)
Now let's calculate the projected world population in 2015 step by step:
Step 1: Find the growth rate in decimal form
2 percent can be converted to a decimal by dividing it by 100, so the growth rate in decimal form is 0.02.
Step 2: Calculate the time difference
We need to find the difference between 2015 and 1987, which is 2015 - 1987 = 28 years.
Step 3: Substitute the values into the formula and solve
P(2015) = 5 billion * (1 + 0.02)^28
To calculate this value, you will need a calculator or you can use an online calculator. Once you perform the calculation, you will find the projected world population in 2015.
To find the projected world population in 2015, we can use the exponential growth formula:
P(t) = P0 * (1 + r)^t
Where:
P(t) is the population at time t
P0 is the initial population
r is the annual growth rate
t is the number of years
Given:
Initial population in 1987, P0 = 5 billion
Annual growth rate, r = 2% = 0.02
Number of years, t = 2015 - 1987 = 28
Substituting the values into the formula:
P(2015) = 5 billion * (1 + 0.02)^28
Now we can calculate the projected world population in 2015:
P(2015) = 5 billion * (1.02)^28
Using a calculator or software, we find:
P(2015) ≈ 7.97 billion
Therefore, the projected world population in 2015 is approximately 7.97 billion.