lanedance said:how do you find p(0) without knowing k?
try dividing you 2 equations together, then use logs
lanedance said:so dividing the 2 equations gives
[tex] e^{6k} = 10 [/tex]
can you solve for k?
you should get some constant a such that
[tex]k = \frac{1}{a} ln(10) [/tex]
the equation then becomes
[tex]p(t) = p(0).e^{kt} = p(0).e^{(t/a) ln(10)} = p(0).e^{ln(10^{t/a}} = p(0) .10^{t/a}[/tex]
[tex]p(0) = p(2).10^{-2/a}[/tex]
which gives me the same p(0) value as you, so your way was fine
lanedance said:i would take the growth rate to mean p'(t)
Population growth refers to the change in the number of individuals in a particular population over a certain period of time. It can be positive, meaning the population is increasing, or negative, meaning the population is decreasing.
There are several factors that contribute to population growth, including increased birth rates, decreased death rates, and immigration. Changes in these factors can lead to fluctuations in population growth over time.
Population growth can be a concern for several reasons. It can put pressure on resources and infrastructure, leading to issues such as food and water shortages, housing problems, and environmental degradation. It can also impact economic and social systems, potentially leading to inequality and conflicts.
Population growth is typically measured using the natural increase rate, which is calculated by subtracting the death rate from the birth rate. It can also be measured using the total fertility rate, which is the average number of children born to a woman in her lifetime, or the net migration rate, which is the difference between immigration and emigration.
The current global population growth rate is estimated to be around 1.1% per year. However, this varies greatly between countries and regions. Some countries have high population growth rates due to high birth rates, while others have negative growth rates due to low birth rates and aging populations.