Answer :
The correct equation to represent the population (in millions), "P(t)," t years after 1995, is P(t) = 51.7 - 45.6t (Option 1), as it provides a linear relationship between population and time in accordance with the given information.
The population equation should represent the population (in millions) at a given time, "t" years after 1995. In this context, it's important to have a linear relationship with time because population changes over time are usually modeled as linear or exponential growth/decay.
The correct equation to represent the population would be:
P(t) = 51.7 - 45.6t
This equation suggests that the population starts at 51.7 million in 1995 (when t = 0) and decreases by 45.6 million each year.
Let's analyze the other options to see why they are not correct:
P(t) = 51.7 - 45.6/t: This equation doesn't represent a population change over time but rather a population change that depends on the reciprocal of time, which doesn't make sense in this context.
P(t) = 45.6 - 51.7t: This equation implies a starting population of 45.6 million in 1995 and decreases by 51.7 million each year, which doesn't match the given information.
P(t) = 45.6 - 51.7/t: Similar to option 2, this equation also depends on the reciprocal of time and doesn't represent a realistic population model.
So, the correct equation for the population (in millions) "t" years after 1995 is P(t) = 51.7 - 45.6t, which represents a decreasing population over time.
To know more about population, refer here:
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