Question

A dog begins his stay at the kennel with 25 fleas. Each day, the number of fleas triples. Which of the following statements is true about the function that represents this situation?

The relationship is linear with an increase of 3 fleas per day.
The relationship is exponential, and the number of fleas increases by a factor of 3 per day.
The relationship is exponential, and the number of fleas increases by a factor of 25 per day.
The relationship is linear with an increase of 75 fleas per day.

Answer 1

It is the second statement.

Explanation:

y = 25(3)^(n - 1) where y = the number of fleas and n = the number of days.

On day 1, y = 25 3^0 = 25

On day 2, y = 25(3^1 = 75

On day 3, y = 25(3) ^2 = 225 and so on.

Exponential growth.

Answer 2

Answer: Second Option

Explanation:

Initially there are 25 fleas, and each day triples the amount.

So:

Day 1: 25

Day 2:
`25 * 3 = 75`

Day 3:
`25 * (3) ^ 2 = 225`

Day 4:
`25 * (3) ^ 3 = 675`

Day n:
`25 * (3) ^ {n-1}`

Note that the function that models the number of fleas for day n is an exponential growth function with an increase factor of 3 and an initial quantity of 25. Therefore, the answer is the second option.