To solve this problem, we can model the population decrease using a linear equation because the population is decreasing at a constant rate. Here's the step-by-step process:

Step 1: Define Variables

Let $P(t)$ represent the population at year $t$. We know the population values for two points in time:

• In 2010 ($t = 2010$), the population was 5,100.
• In 2013 ($t = 2013$), the population was 3,300.

Step 2: Determine the Rate of Decrease

The rate of decrease (slope, $m$) can be found using the formula for the slope between two points $(t_1, P_1)$ and $(t_2, P_2)$:

$m = \frac{P_2 - P_1}{t_2 - t_1} = \frac{3300 - 5100}{2013 - 2010} = \frac{-1800}{3} = -600$

This tells us the population decreases by 600 people per year.

Step 3: Write the Linear Equation

The linear equation for the population can be written as:

$P(t) = m(t - t_1) + P_1$

Substituting $m = -600$, $t_1 = 2010$, and $P_1 = 5100$:

$P(t) = -600(t - 2010) + 5100$

Step 4: Predict the Population in 2016

Now, substitute $t = 2016$:

$P(2016) = -600(2016 - 2010) + 5100 = -600 \times 6 + 5100 = -3600 + 5100 = 1500$

So, the predicted population in 2016 is 1,500.

Would you like further details or have any questions?

Related Questions:

1. What would be the population in 2020 if the trend continues?
2. How long will it take for the population to reach zero at this rate?
3. Can you represent the population decrease on a graph?
4. What is the population rate of decrease as a percentage per year?
5. How would the prediction change if the decrease rate was not constant?

Tip: When working with linear models, always identify the slope first as it tells you how fast the quantity is changing over time!