Question

A study done from 1950 through 2000 estimated that the world population increased on average by 1.77% each

year. In 1950, the world population was 2,519 million.
a. Write a formula for the world population t years after 1950. Use pp to represent the world population.
b. Write a formula for the number of years it takes to reach a population of p.
c. Use your equation in part (b) to find when the model predicts that the world population is 10 billion.

Answer 1

a.
`p = 2.519*(1.0177^(t))`

b.
`t =(log((p)/(2.519)) )/(log(1.0177))\\`

c. in the year of 2029

Explanation:

The world population in 1950 was 2,519 million or 2.519 billion.

a-) Population after 1950 can be defined as a compounded growth at the rate of 1.77% per year. This can be modeled as follows:

`p = 2.519*(1.0177^(t))`

b-) To find an expression for the number of years to reach a population p, we must apply logarithmic properties to the expression found in part a. as follows:

`p = 2.519*(1.0177^(t))\\log(p) = log(2.519*1.0177^(t))\\log(p) = log(2.519) + log(1.0177^(t))\\log(p) = log(2.519) + t*log(1.0177)\\\\t = (log(p) - log (2.519))/(log(1.0177)) \\t =(log((p)/(2.519)) )/(log(1.0177))`

c-) For p = 10:

`t =(log((10)/(2.519)) )/(log(1.0177))\\t = 78.58`

The model predicts that the world population will surpass 10 billion in roughly 79 years from 1950, that is in the year of 2029.