Question

Rakeem is researching a population of fruit flies. He observes the number of fruit flies present every other day for one week and records the data in the table shown. What is the average rate of change in the number of fruit flies present between Day 3 and Day 5?

Answer 1

The average rate of change in the number of fruit flies present between Day 3 and Day 57 is 15,200 fruit flies per day.

1. We are interested in the average rate of change between Day 3 and Day 57. This means we need to find the difference in the number of fruit flies present on those two days and divide it by the number of days that have passed.

2. On Day 3, there are 400 fruit flies. On Day 57, there are 160,000 fruit flies.

3. The difference in the number of fruit flies is 160,000 - 400 = 159,600 fruit flies.

4. The number of days that have passed is 57 - 3 = 54 days.

5. Therefore, the average rate of change is 159,600 fruit flies / 54 days = 2,955.56 fruit flies per day.

6. Round to the nearest hundredth: 2,955.56 fruit flies per day ≈ 2,956 fruit flies per day.

So, the average rate of change in the number of fruit flies present between Day 3 and Day 57 is 2,956 fruit flies per day. This means that the population of fruit flies was increasing by an average of 2,956 flies each day during that time period.

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