Question

The graph show the population of beavers in a forest for different numbers of years after

1995. The beaver population is growing exponentially.

Explain why we can think of the beaver population as a function of time in years.
2. What is the meaning of the point labeled Q in this context?
3. Write an equation using function notation to represent this situation.

Answer 1

1. We can think of the beaver population as a function of time in years because it shows how the population changes over time. The graph shows a direct correlation between the number of years after 1995 and the number of beavers in the forest, indicating that the population of beavers is dependent on the number of years that have passed since 1995.

2. The point labeled Q represents the exponential growth rate of the beaver population.

3. An equation using function notation to represent this situation would be: P(t) = P0 * e^kt, where P(t) is the population at time t (in years after 1995), P0 is the initial population of beavers in 1995, and k is the constant exponential growth rate.