Question

In your discussion post, think about some examples of exponential growth in the real world. They might be examples from science, medicine, or finances. Share two examples of exponential growth, and include a description of who would benefit from the information found in these examples. Also include, two examples of careers and jobs that would be difficult to work in if you didn't understand exponential growth. Describe why it would be difficult in these specific examples.

Answer 1

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. For example, if a population of mice doubles every year starting with two in the first year, the population would be four in the second year, 16 in the third year, 256 in the fourth year, and so on. The population is growing to the power of 2 each year in this case (i.e., exponentially).

Assume you deposit $1,000 in an account that earns a guaranteed 10% rate of interest. If the account carries a simple interest rate, you will earn $100 per year. The amount of interest paid will not change as long as no additional deposits are made.

If the account carries a compound interest rate, however, you will earn interest on the cumulative account total. Each year, the lender will apply the interest rate to the sum of the initial deposit, along with any interest previously paid. In the first year, the interest earned is still 10% or $100. In the second year, however, the 10% rate is applied to the new total of $1,100, yielding $110. With each subsequent year, the amount of interest paid grows, creating rapidly accelerating, or exponential, growth. After 30 years, with no other deposits required, your account would be worth $17,449.40.

variety of examples of exponential growth as it applies to the real world. For example, a man is believed to have brought 24 rabbits to Australia in the 1800s so that he could hunt them; however, rabbits have no natural predators in Australia, and so the population grew out of control. Within ten years, so many rabbits had descended from these 24 first rabbits that millions could be killed without making a dent in the population.

The real secret to exponential growth is this - not only do rabbits have children, but their children have children, as do their children's children. The new growth increases just as fast as the growth you started with. There is nothing to slow the growth down or bring it to a halt.

When graphed, exponential growth always looks like it is starting off slowly and then rapidly becomes steeper:

Graph of Exponential Growth