Chapter 3, Problem 4PS

To determine

To explain: The meaning that a quantity grows exponentially.

Answer to Problem 4PS

When a quantity grows exponentially it is meant that rate of growth increases with increase in quantity.

Explanation of Solution

Given information:

The exponential function and polynomial functions.

The exponential function increases rapidly when compared with polynomial functions.

For a given value of x, the value of $e^x$ is greater than value of $x^n$ , where n is natural number.

For instance, when $x=100$ , the values obtained by the functions $y_1=e^x\text{ and }{y}_2=x^2$ are as follows, $y_1=2.6\times {10}^{43}\text{ and }{y}_2=10000$ . So, at a given point in time rate of growth is proportional to the amount at that time.

Therefore, when a quantity grows exponentially it is meant that rate of growth increases with increase in quantity.