Question

4. The population (in millions) of a country at t years after 1980 is given by P(t) = 23.42 00154 a) What was the population in 1980? b) What was the expected population in 2005. c) When, to the nearest year, will the country have a population of 60 million?

Answer 1

$a) \text{ Put t=0 to find the population in 1980};\\ P(0)=23.4\ millions$

b) Put t=25 to find the population in 2005; P(25) = 23.4e" 0.0154x25 34.39 millions

$c) \text{ Let after t years from 1980 the population is 60 millions, then};\\ 60=23.4e^{0.0154t}\\ \implies e^{0.0154 t}=2.5641025641\\ \text{ Taking logarithm on both sides};\\ 0.0154t=0.94160\\ \implies t=61.14\approx 61\\ \color{red}\text{ Thus after 61 years from 1980 i.e. in 2041 the population will become 60 millions}$