A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7b^t , where t is the time in weeks after the release and b is a positive unknown base. After observing the population growth over a few weeks, the exponential function P(t) = 7(2)^t is used to model the growth. Interpret the significance of 2 in the function as it applies to the situation.

Question

A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7b^t , where t is the time in weeks after the release and b is a positive unknown base. After observing the population growth over a few weeks, the exponential function P(t) = 7(2)^t is used to model the growth. Interpret the significance of 2 in the function as it applies to the situation.
Responses
A	The population is doubling each week.The population is doubling each week.
B	The population is doubling each month.The population is doubling each month.
C	The population is counted every 2 weeks.The population is counted every 2 weeks.
D	The population is increasing by 2 fish each week.

GPT-4o mini · Answer

The correct interpretation of the significance of 2 in the function \( P(t) = 7(2)^t \) is:

A The population is doubling each week.

This is because the base \( b = 2 \) indicates that for each week (each increment of \( t \) by 1), the population \( P(t) \) is multiplied by 2, meaning it doubles.