The population of trees in a forest decreases by 6% every 4 years. The population at the beginning of 2015 was estimated to be 14,000. If p represents the population t years after 2015, which equation gives the population of trees over time?

Correct answer: p = 14000(0.94)^(t/4). A 6% decrease leaves 94% (0.94) every 4 years, and there are t/4 such periods in t years, so p = 14000(0.94)^(t/4).

Background: Exponential decay has the form: final = initial × (decay factor)^(number of periods).

• p = 14000(0.06)^(t/4): 0.06 is the amount lost, not the amount remaining.
• p = 14000 + 0.94(4t): This describes a linear change, not an exponential decay.
• p = 14000(0.94)^(4t): The exponent 4t counts four periods per year instead of one period per four years.

Did you know? Here the decay factor is 1 − 0.06 = 0.94.

Memory trick: Decay factor = 1 − rate.