Question

Use an annual growth rate of 1.6% in a 40 year period for a certain population to find the approximate doubling time and then predict the population in 2050, based on a 2000 population of 6.0 billion. What is the approximate doubling time? What will be the approximate population in 2050?

Answer 1

- the approximate doubling time is 43.3216 ≈ 43

- the approximate population in 2050 is 13.353 billions

Explanation:

Given that;

growth rate r = 1.6% = 0.016

so,

Doubling time = In2 / 0.016 = 43.3216

Hence, the approximate doubling time is 43.3216 ≈ 43

Population in 2050;

t = 2050 - 2000 = 50

po = 6 billion

r = 0.016

so

p = po
`e^(rt)`

we substitute

p = 6
`e^(0.016*50)`

p = 6
`e^(0.8)`

p = 6( 2.2255 )

p = 13.353 billions

Therefore, the approximate population in 2050 is 13.353 billions