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?

A. The relationship is linear with an increase of 3 fleas per day.
B. The relationship is exponential, and the number of fleas increases by a factor of 3 per day.
C. The relationship is exponential, and the number of fleas increases by a factor of 25 per day.(WRONG)
D. The relationship is linear with an increase of 75 fleas per day. (WRONG)

Answer 1

B. The relationship is exponential

Answer 2

The relationship is exponential, and the number of fleas increases by a factor of 3 per day.

Explanation:

Given :A dog begins his stay at the kennel with 25 fleas. Each day, the number of fleas triples.

Solution:

Let x denotes the number of days

Initial number of fleas = 25

Each day, the number of fleas triples.

The given situation represents the exponential function

General form=
`y=ab^x`

where a is the initial amount and b is the rate factor

So, a = 25

b =3

So, function :
`y=25(3)^x`

Thus Option B is correct.

Hence The relationship is exponential, and the number of fleas increases by a factor of 3 per day.