1. Exponential and Logarithmic Functions and Their Applications

In 2008, the black bear population in Granit Park was 510, and the population growth rate was 5% yearly.

Recall the exponential growth model:

P(t) = P₀e^kt where P(t) is the population at time t (in years)

t is the number of years since the initial year

P₀ is the population at the initial year t = 0

K is the exponential growth rate (in decimal form)

1. Write the exponential growth function that represents a model for the black bear population.

2. According to this model, what will be the black bear population in 2025?

3. In what year will the black bear population reach 850?