6. The population of a certain bacteria can be modeled by the function P(t)=2000(1.034)^t where t represents the number of hours after an experiment has started. What does 2,000 represent in the function?
Answer: C
2,000 represents the population of bacteria when the experiment started.
In the function P(t)=2000(1.034)^t, the value 2,000 signifies the initial population of bacteria at the start of the experiment, which corresponds to t=0.
A) The amount of time the experiment lasts
This option is incorrect because the function does not provide any information regarding the duration of the experiment. Instead, it focuses on the population growth over time.
B) The population of bacteria when the experiment ends
This choice is incorrect as 2,000 refers to the initial population at the beginning of the experiment, not the population at its conclusion. The population at the end would depend on the value of t.
C) The population of bacteria when the experiment started
This option is correct because, in the given function, 2,000 is the constant that indicates the initial number of bacteria present at time t=0.
D) The percent the population of bacteria changes every hour
This option is incorrect since the function's growth rate is represented by the base of the exponent, 1.034, which indicates a growth factor, not a percentage change. The percent change can be derived from this factor, but it is not directly represented by the value 2,000.
Conclusion
The correct answer clearly identifies that 2,000 is the initial population of bacteria at the start of the experiment. All other options misinterpret the significance of this value within the context of the growth model, as they either relate to time or improperly assign the population to different phases of the experiment.