Answer:
In the expression 250(1/2)^t/4, the following meanings can be attributed to the numbers:
250: This is the initial amount of caffeine in milligrams present in the coffee when it was brewed.
(1/2): This is the decay factor or the rate at which the caffeine content decreases over time. In other words, it represents the fraction of caffeine that remains after each hour. Here, the expression (1/2)^t means that the caffeine content will decrease by a factor of 1/2 after each hour.
t: This represents the time elapsed in hours since the coffee was brewed.
4: This is a scaling factor or a unit conversion factor used to convert the expression into milligrams. The expression 250(1/2)^t/4 represents the amount of caffeine remaining in milligrams after t hours.
To summarize, the expression 250(1/2)^t/4 models the amount of caffeine remaining in a coffee after t hours, where 250 is the initial amount of caffeine in milligrams, (1/2) is the decay factor or the fraction of caffeine that remains after each hour, t is the time elapsed in hours, and 4 is the scaling factor used to convert the expression into milligrams.
Among the answer choices provided, the second one is the most accurate:
250 represents the amount of caffeine in a body. 1/2 represents the decay rate of the caffeine. 4 represents the amount of hours it takes for the caffeine to reach its half-life.
The given expression 250(1/2)^t/4 models the amount of caffeine remaining in a coffee after t hours, where 250 is the initial amount of caffeine in milligrams, (1/2) is the decay factor or the fraction of caffeine that remains after each hour, t is the time elapsed in hours, and 4 is the scaling factor used to convert the expression into milligrams. Therefore, the answer choices that mention coffee consumption or growth factor of coffee are not correct in this context.
In this expression, the fraction 1/2 represents the decay rate or the fraction of caffeine that remains after each hour. The number 4 is used to scale the expression into milligrams and does not represent the half-life of caffeine. The half-life of caffeine is the amount of time it takes for half of the initial caffeine amount to decay, and it can be calculated using the formula t1/2 = ln(2) / k, where k is the decay constant.