Final answer:
To predict the population of Tallahassee for 2025 and 2030, we first solve for 'k' using the population data from 2008, then using the exponential model, we calculate the populations for future years by substituting 't' with the respective years.
Step-by-step explanation:
The question concerns the application of an exponential growth model to predict populations of Tallahassee, Florida, in the future years based on a given formula P = 152.7ekt and an initial population in the year 2000. Using this model, we can find the growth factor 'k' by substituting the known population for the year 2008. With 't' being 8 (since 2008 - 2000 = 8 years), the population 171.847 (in thousands) gives us the equation 171.847 = 152.7e8k. Solving for 'k', we can then use this value to calculate future populations for the years 2025 and 2030.
To solve for 'k', first divide both sides by 152.7, resulting in
approximately 1.1257 = e8k. Taking the natural logarithm of both sides,
ln(1.1257) = 8k, we find that k is approximately
ln(1.1257)/8. Once 'k' is determined, we substitute 't' with 25 (for the year 2025) and then with 30 (for the year 2030) into the original equation to predict future populations.