2.8: Exponential population model

0606/21/O/N/20 — Question 8 · 8 marks

The population

P

, in millions, of a country is given by

P = A \times b^{t}

, where

t

is the number of years after January 2000 and

A

and

b

are constants. In January 2010 the population was 40 million and had increased to 45 million by January 2013.

(a)

Show that

b = 1.04

to 2 decimal places and find

A

to the nearest integer.

[4]

(b)

Find the population in January 2020, giving your answer to the nearest million.

[1]

(c)

In January of which year will the population be over 100 million for the first time?

[3]