The formula A 101e005t models the population of Los Angeles

The formula A = 10.1e^.005t models the population of Los Angeles, California, A, in millions, t years after 1992. a) What was the population in 1992? b) If the growth rate continues into the future, when will the population reach 14 million? c) What is the expected population of Los Angeles in the year 2010?

Solution

A=10.1 e^.005t

This is of the form A=A₀e^kt

Where A₀ is the initial polulation which is 10.1 here

a. Therefore in 1992 ,population is 10.1 million

b. 14= 10.1 e^.005t

ln(14/10.1)=.005 t

t= ln(14/10.1)/.005

t= 65.3 yrs

So in 2057,the polulation will be 14 million

c. 2010 means t=2010-1992=18

A= 10.1 e^.005*18

A= 11.05 million