Question

The population of a small town in central Florida has shown a linear decline in the years 2005-2013. In 2005 the population was 49100 people. In 2013 it was 46060 people.

a) P= -1080t+49100
b) P= -860t+49100
c) P= -1000t+49100
d) P= -1200t+49100

Answer 1

The equation that represents the population decline in the given scenario is P = -1000t + 49100. This equation can be derived by using the population equation and substituting the given values. The equation shows a linear decline in population over time.

Step-by-step explanation:

The equation that represents the population decline in the given scenario is P = -1000t + 49100.

1. Start with the population equation, P = Po * e^(n*t), where Po is the initial population, n is the growth rate, and t is the time in years.
2. Plug in the given values: Po = 49100 (2005 population), n = growth rate (to be calculated), and t = 2013 - 2005 = 8 years.
3. Rearrange the equation to solve for n: -1000t = ln(Po/P), where P is the population in 2013 (46060 people).
4. Substitute the values and solve for n: -1000 * 8 = ln(49100/46060).
5. Calculate the value of n: n = -8000 / ln(49100/46060).
6. The final equation is P = -1000t + 49100, where t represents the number of years after 2005.