Final answer:
To write an exponential function for quail population growth, we use the formula P = P0ert, substituting the initial population (P0) and growth rate (r). Without specific values, we cannot determine the exact population after 3 years; however, with hypothetical figures, we can estimate the population.
Step-by-step explanation:
Writing an Exponential Function for Quail Population
To model the quail population using an exponential function, we need to know the initial population (P0), the growth rate (r), and the time period in question (t). The general form of an exponential growth model is P = P0ert, where P is the population at time t, P0 is the initial population, e is the base of the natural logarithm, r is the growth rate, and t is the time in years.
If we assume an initial population of P0 and a yearly growth rate of r (expressed as a decimal), and we want to find the population after 3 years (t = 3), the function becomes P = P0er(3).
Without specific figures for the initial population and growth rate, we cannot calculate the exact population after 3 years. However, assuming hypothetical values, let's say P0 = 100 quails and r = 5% (or 0.05), the function becomes P = 100e0.05(3).
To get an approximate population after 3 years, we would evaluate this expression using a calculator or software capable of computing exponentials. If we do the math, we would find P to be approximately 116.18 quails.