**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,
at time
, increases exponentially and the initial population at
is
, for some value
*a*
the process may be modeled by the equation

.

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

.

Hence,

, so
.

If we denote
, we can rewrite the original formula for the population growth as

.

In this quiz, we shall use the first form
.

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

= 3.6 (
).

(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.*