To identify which context represents exponential growth, we need to understand the characteristics of both exponential growth and exponential decay.
1. Exponential Decay:
Exponential decay occurs when the quantity decreases by a constant percentage over equal time periods. One way to express this is through a factor less than 1.
Consider the context: "The amount of a certain medication in a person's bloodstream decreases by [tex]\( \frac{3}{5} \)[/tex] every day."
- Here, "decreases by [tex]\( \frac{3}{5} \)[/tex]" means that the substance reduces to [tex]\( \frac{2}{5} \)[/tex] of its previous amount each day (since [tex]\(1 - \frac{3}{5} = \frac{2}{5}\)[/tex]).
- This scenario is an example of exponential decay because the amount of medication decreases exponentially over time.
2. Exponential Growth:
Exponential growth occurs when the quantity increases by a constant percentage over equal time periods, represented by a multiplication factor greater than 1.
Consider the context: "A population of 150 bacteria triples every week."
- In this case, "triples every week" signifies that the bacteria multiply by a factor of 3 each week.
- This scenario is a clear example of exponential growth because the population grows exponentially over time.
By examining the descriptions provided:
- The first context indicates exponential decay because it describes a reduction in the quantity.
- The second context describes exponential growth because it explains an increase in the population.
Therefore, the context that represents exponential growth is:
"A population of 150 bacteria triples every week."
So, the correct answer is option 2.
