Final Answer:
The population of Bald Knob, AR, after t years, is given by the function P(t) = 1693 + 22e^(0.08t), where t ≥ 0 and t = 0 corresponds to the initial time.
Step-by-step explanation:
The given function P(t) = 1693 + 22e^(0.08t) represents the population of Bald Knob, AR, at any time t in years. The term 1693 corresponds to the initial population, and 22e^(0.08t) represents the growth factor. The exponential term e^(0.08t) signifies continuous growth at a rate of 8% per year.
To understand the initial population, we look at the constant term 1693. When t = 0, the initial time, the population is P(0) = 1693 + 22e^(0.08 * 0) = 1693 + 22 * 1 = 1715. Therefore, the population at the starting point is 1715.
The exponential term e^(0.08t) influences the growth rate. As t increases, the population grows exponentially due to the continuously compounding nature of the function. The coefficient 22 scales this growth. The larger t becomes, the more significant the exponential term contributes to the overall population.
In summary, the function P(t) = 1693 + 22e^(0.08t) accurately models the population growth of Bald Knob, AR, where t is the time in years, and P(t) gives the population at any given time. The initial population is 1715, and the exponential term accounts for continuous growth at a rate of 8% per year.