The population of a bacteria colony can be modeled by the function P(x)=6(4)^x, where x is the number of days.

Question

Which statement best interprets one value in the function

The bacteria population increases one value in the function

The initial population of the bacterium is 24

The bacteria population increases by a factor of 4 each day

The initial population of the bacteria is 4

Answer 1

To interpret the function \( P(x) = 6(4)^x \), let's analyze its components:

• The function gives you the population \( P(x) \) after \( x \) days.
• The term \( 6 \) is the initial population of the bacteria when \( x = 0 \) since \( P(0) = 6(4)^0 = 6(1) = 6 \).
• The term \( (4)^x \) indicates that for each passing day, the population increases by a factor of 4.

Now, let's evaluate each statement:

1. The bacteria population increases one value in the function.
   This statement is vague and does not accurately describe the growth.

2. The initial population of the bacterium is 24.
   This is incorrect. The initial population when \( x = 0 \) is 6.

3. The bacteria population increases by a factor of 4 each day.
   This statement is accurate; as \( x \) increases by 1 (each day), \( P(x) \) is multiplied by 4.

4. The initial population of the bacteria is 4.
   This is incorrect. The initial population is 6.

The statement that best interprets one value in the function is:

The bacteria population increases by a factor of 4 each day.