The equation you provided is in the form of a linear function:

\[
P(t) = -3.45(t - 2010) + 84.9
\]

Where \( P(t) \) represents a quantity (such as population, price, or any other dependent variable) at time \( t \). 

To solve for \( P(57.5) \), we substitute \( t = 57.5 \) into the equation:

\[
P(57.5) = -3.45(57.5 - 2010) + 84.9
\]

Now, let's calculate this step by step:

1. Subtract 2010 from 57.5:
   \[
   57.5 - 2010 = -1952.5
   \]

2. Multiply this result by -3.45:
   \[
   -3.45 \times -1952.5 = 6735.125
   \]

3. Add 84.9 to the result:
   \[
   P(57.5) = 6735.125 + 84.9 = 6820.025
   \]

So, \( P(57.5) = 6820.025 \).

Would you like more details on this calculation or have any other questions?

Here are 5 related questions:

1. What does the function \( P(t) \) represent in this context?
2. How does changing the coefficient \(-3.45\) affect the slope of the function?
3. What happens to \( P(t) \) as \( t \) approaches 2010?
4. Can we interpret the intercept \( 84.9 \) in a meaningful way?
5. What would \( P(t) \) equal when \( t = 2010 \)?

**Tip:** When interpreting linear equations, always identify the slope and intercept, as they reveal crucial information about the relationship between variables.

Learn how to solve the linear function P(57.5) = -3.45(t - 2010) + 84.9 with a step-by-step solution. This problem involves key algebraic concepts such as linear functions and substitution. Suitable for students in Grades 9-12.

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