Exponential Growth--An Example

Many real life phenomena are modeled by exponential functions: uninhibited population growth, balance on an account with interest compounded continuously, etc. Below, we look at an example of population growth.

Each process of exponential growth can be written in two ways: in terms of a given base a , or in terms of the natural base e . For example, if certain population, [Maple Math] at time [Maple Math] , increases exponentially and the initial population at [Maple Math] is [Maple Math] , for some value a the process may be modeled by the equation

[Maple Math] .

The same equation can be rewritten in terms of e. Indeed, we have

[Maple Math] .


[Maple Math] , so [Maple Math] .

If we denote [Maple Math] , we can rewrite the original formula for the population growth as

[Maple Math] .

In this quiz, we shall use the first form [Maple Math] .

Problem 1. The population, [Maple Math] , in millions, of Nicaragua was 3.6 millions in 1990 and is growing exponentially. Let [Maple Math] be the time, in years, since Jan. 1, 1990. Suppose the population at time [Maple Math] is given by

[Maple Math] = 3.6 ( [Maple Math] ).

(a) If the trend continues, what will the population be on Jan.1, 2005?

(b) When will the population reach 9 million?

(c) How long will it take for the population to double?

Solutions to Problem 1.


MTH 111 Quizzes, B. Kaskosz and L. Pakula, 2001.