Final answer:
To find the pheasant population in 2015, we calculate the exponential decay from the year 2009 using the decay rate of 1.7% over 6 years. Plugging in the values into the exponential decay formula, we find that the closest estimate is 4150.
Step-by-step explanation:
The question involves calculating the decline of a pheasant population using a percentage rate decrease. To predict the population in the year 2015, we use the formula for exponential decay:
P = P0e(r)(t)
Where:
- P is the future population size
- P0 is the initial population size
- r is the rate of decline (as a decimal)
- t is the time in years since the initial time
Given:
- P0 = 4600 (Initial population in 2009)
- r = -0.017 (Decline rate of 1.7%)
- t = 2015 - 2009 = 6 years
Plugging the values in, we get:
P = 4600e(-0.017)(6)
Calculating the above expression, we will get:
P = 4600 * e-0.102
P = 4600 * 0.9028 (approximately)
P ≈ 4153.25
Thus, the closest prediction for the population in the year 2015 is 4150.