We have the linear function modeling the population:

$f(x) = 2.945x + 269.827$

where $x$ is the number of years after 2000, and $f(x)$ represents the population in millions.

Part (c): Predict the population in 2080

Since 2080 corresponds to $x = 2080 - 2000 = 80$, we substitute $x = 80$ into the function:

$f(80) = 2.945(80) + 269.827$

$= 235.6 + 269.827$

$= 505.4$

Final Answer:

The projected population in 2080 will be 505.4 million.

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Would you like a step-by-step breakdown of how this function was derived?

Here are five related questions to explore further:

1. How would the model change if population growth slowed after 2050?
2. What is the rate of change in population according to this model?
3. How accurate do you think a linear model is for long-term predictions like this?
4. Could an exponential or logistic model be a better fit? Why or why not?
5. If the population growth rate increased, how would that affect the function?

Tip:

Linear models work well for short-term projections, but for long-term trends, consider using exponential or logistic models to account for real-world constraints like resource limits. 🚀