To represent this situation as an exponential model, we use the general form of an exponential decay function:

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

Where:

• $P$ is the population after $t$ years,
• $P_0$ is the initial population,
• $r$ is the rate of decrease (in decimal form),
• $t$ is the time in years.

Given:

• $P_0 = 10,000$,
• $r = 0.07$ (7% annual decrease),

The exponential model is:

$P = 10,000 (1 - 0.07)^t$

Simplify:

$P = 10,000 (0.93)^t$

Final model:

$P = 10,000 (0.93)^t$

Would you like me to provide a graph or calculate specific values?

Related Questions:

1. What is the population after 5 years?
2. How long will it take for the population to decrease to half of its initial size?
3. What is the population decrease between year 1 and year 2?
4. How does the decay factor (0.93) impact the population over time?
5. What would the model look like if the decrease were 10% annually instead of 7%?

Tip:

Always verify the decay rate in exponential models by checking if it aligns with the percentage given in the problem.