To solve this question, let's analyze it step-by-step:

Problem Breakdown

1. We know:

   • In 1995, the moose population was 1900.
   • By 1996, the population increased to 2000.
   • We assume the population grows linearly.

2. We need:

   • A formula for the population $P$ as a function of $t$, where $t$ represents the years since 1990.
   • A prediction for the population in the year 2003.

Step 1: Determine the Linear Growth Formula

Since the population is changing linearly, we can use the formula for a linear function: $P = mt + b$ where:

• $P$ is the population,
• $t$ is the number of years since 1990,
• $m$ is the slope (rate of change of the population per year),
• $b$ is the y-intercept (initial population in 1990).

Convert Years to $t$-values

• 1995 corresponds to $t = 5$ (since 1995 is 5 years after 1990).
• 1996 corresponds to $t = 6$.

Find the Slope $m$

The population changes from 1900 to 2000 between $t = 5$ and $t = 6$, so: $m = \frac{2000 - 1900}{6 - 5} = \frac{100}{1} = 100$ Thus, the population increases by 100 moose per year.

Determine the Intercept $b$

Using the point $(t = 5, P = 1900)$: $1900 = 100 \cdot 5 + b$ $1900 = 500 + b$ $b = 1400$

Step 2: Write the Formula

Now we have the formula: $P = 100t + 1400$

Step 3: Predict the Population in 2003

For 2003, $t = 13$ (since 2003 is 13 years after 1990): $P = 100 \cdot 13 + 1400$ $P = 1300 + 1400 = 2700$

Final Answer

• Formula: $P = 100t + 1400$
• Predicted Population in 2003: 2700 moose

Would you like further details or have any other questions?

Here are some related questions to deepen understanding:

1. How would the formula change if the population grew exponentially instead of linearly?
2. If the population had increased by 150 instead of 100 each year, what would the new formula be?
3. What would the population be predicted in 2010 based on this model?
4. Can you determine the year when the population would reach 3000 moose?
5. How would the answer change if the starting population in 1995 had been 1800 instead of 1900?

Tip: For linear growth problems, focus on finding the rate of change and using it consistently across time intervals.