Which of the contexts below represents exponential growth?AnswerMultiple Choice AnswersA population of 150 bacteria quadruples every week.David puts $50 a month into a savings account.A car depreciates at a rate of 2.6% per year.A town's population shrinks at a rate of 2.4% every year.
Question
Which of the contexts below represents exponential growth?AnswerMultiple Choice AnswersA population of 150 bacteria quadruples every week.David puts $50 a month into a savings account.A car depreciates at a rate of 2.6% per year.A town's population shrinks at a rate of 2.4% every year.
Solution
The context that represents exponential growth is "A population of 150 bacteria quadruples every week."
Here's why:
Exponential growth refers to an increase based on a constant rate of growth over a given period of time. In this case, the bacteria population is not just increasing, but the rate of increase is getting larger every week (it's quadrupling, or growing by 400%, each week). This is a clear example of exponential growth.
On the other hand, David's savings account is growing linearly, because he's adding the same amount of money each month. The car's value and the town's population are both decreasing, not growing, and they're doing so at a constant rate (2.6% and 2.4% per year, respectively), which is a linear, not exponential, rate of decrease.
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