The question in the image asks for the correct model to represent the population of deer growing at a rate of 8% per year, starting from an initial population of 500 in 2016.

To model population growth with a constant percentage increase, we use the exponential growth formula:

$P(t) = P_0 (1 + r)^t$

Where:

• $P(t)$ is the population at time $t$,
• $P_0$ is the initial population (500 in this case),
• $r$ is the growth rate (8% = 0.08),
• $t$ is the number of years after the starting point (2016).

Thus, the equation becomes:

$P(t) = 500 (1 + 0.08)^t = 500 (1.08)^t$

The correct model is:

$P(t) = 500 (1.08)^t$

From the given choices, the third option ( $P(t) = 500 (1.08)^t$ ) is the correct one.

Would you like more details or have any questions? Here are five related questions to expand on this concept:

1. How would the model change if the growth rate were 5% instead of 8%?
2. What is the population of deer after 5 years using the given model?
3. How does the exponential growth formula differ from linear growth?
4. Can exponential decay be modeled similarly? How would the formula change for a decay rate?
5. What happens to the population if the growth rate is negative?

Tip: Always make sure to express percentage growth as a decimal in the exponential growth formula!