Answer:
The exponential decay function of the rabbit population P(t) can be expressed as:
P(t) = 144,000 * e^(-0.072t)
Explanation:
Where t is the time in years.
This function represents the expected decrease in the rabbit population of Springfield, Ohio, assuming a constant rate of decline of about 7.2% per year. The initial population of rabbits in 2016 was 144,000, and this number is multiplied by the exponential factor e^(-0.072t), which represents the proportion of rabbits that will remain after t years.
As time passes, the value of P(t) will decrease exponentially, reflecting the declining rabbit population. For example, after one year (t=1), the rabbit population is expected to be:
P(1) = 144,000 * e^(-0.072*1) = 133,632
This means that the rabbit population is expected to decrease by about 10,368 rabbits in the first year.
The exponential decay function is commonly used in many fields to model phenomena that exhibit exponential decay over time, such as radioactive decay, bacterial growth, and population dynamics.