Question

Assuming that the world population continue to grow at its current rate, how many years would it take for the world population to grow.

Hint: rate of natural increase: 0.012 is the value of "r" that you will use in the calculations below.

Remember, net migration is 0 at the global level, so the rate of natural increase (RNI) is the growth rate(r) for the world population.

Second, what is the size of the world population in 2018, according to the world population datasheet?

P₂₀₁₈ = 7,621,000,000

Now, Use the Exponential Grown Rate formula and solve for n.

A.) How long would it take to grow by 50%

B.) How long would it take to Quadruple?

C.) How long would it take to add the next 1 billion?

Answer 1

If we are given exponential growth rate, The population after a time n can be given by

P = P_o e^rn

Where P₀ is the initial population

r is exponential growth rate

n is time

we know that value of e = 2.71828

and log e = 0.434294

We can calculate the log values in the excel by the formula =log (number, base)

base will be 10 here

Question (a)

given growth rate = 0.0012

P should be 1.5 times of P₀ if P₀ has to grow by 50%

1.5P₀ = P₀ e^0.012n

1.5 = e^0.012n

Applying logarithms on both sides we get

log (1.5) = 0.012*n*(log e)

0.176091 = 0.012 * n * 0.434294

So n = 0.176091 / (0.012 * 0.434294)

= 0.176091 / 0.005212

= 33.78878

So it would take approximately 33.79 years for the population to increase by 50%

Question (b)

For Population to Quadraple

P should be 4P₀

4P_{0 =} P₀ e^0.012n

4 = e^0.012n

Applying logarithms on both sides we get

log 4 = 0.012 * n * log e

0.60206 = 0.012 * n * 0.434294

n = 0.60206 / 0.012 * 0.434294

= 115.524

So approximately after 115.52 years the population will quadraple

Question (c)

Time taken to add 1 billion people

Here P will be 1 billion + P₀

So P will be 1,000,000,000 + 7,621,000,000 = 8,621,000,000

So

8,621,000,000 = 7,621,000,000 e^0.012n

8,621,000,000 /  7,621,000,000 = e^0.012n

1.3121 = e^0.012n

Applying logarithms on both sides we get

log 1.3121 = 0.012 * n * log e

0.05354 = 0.012 * n * 0.434294

n = 0.05354 / 0.012 * 0.434294

= 10.27446

So approximately after 10.28 years 1 billion more population will be added