Question

At the veterinarian's office, Pam read that the number of fleas on a house pet can triple each week if left untreated. She wonders how many fleas her dog would have in a few weeks if she found 6 fleas on him today. You can use a function to approximate the total number of fleas Pam's dog would have x weeks from now. Is the function linear or exponential? Which equation represents the function?

Answer 1

The growth of the number of fleas on Pam's dog can be described as exponential because the number of fleas triples each week. In general, exponential growth can be represented by the formula:

\[ N(t) = N_0 \cdot r^t \]

Where:

• \( N(t) \) is the number of fleas at time \( t \),
• \( N_0 \) is the initial number of fleas,
• \( r \) is the growth factor (in this case, since the number triples, \( r = 3 \)),
• \( t \) is the time in weeks.

For Pam's dog:

• The initial number of fleas (\( N_0 \)) is 6.
• The growth rate (\( r \)) is 3.

Plugging these values into the formula, we get:

\[ N(t) = 6 \cdot 3^t \]

This function, \( N(t) = 6 \cdot 3^t \), represents the exponential growth of the number of fleas on Pam's dog, where \( t \) is the number of weeks into the future.

In summary:

• The function is exponential.
• The equation representing the function is \( N(t) = 6 \cdot 3^t \).