I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 41990 to 33,871 in 42000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: *In thousands
P = Ce^{rt} I want to find r
Plugging in the numbers:
To check: Here's where I question my logic or math. Let's say that back in 41990 Californina implemented a conservation drive that by 42000 the entire population would conserve 20% of some resource. We'll have X = total amount of the resource. That is to say that in 41990 the combined consumption of 29760 people for that year was X. By 42000 they want X reduced by 20% or X*.80. But, we need to include population growth so:
Real Percent = .80Xe^{rt}
P = .80Xe^{0.012939398*10} Does this seem correct? Any help towards coming up with a correct answer would be greatly appreciated. Steve
Level of question 12+? I am glad you asked for "help towards coming up with A correct answer" as the answer depends on the exact question being asked. What you have is a correct answer, but not to the question as I understand it. I came up with your "Real Percent" and hence your answer with the following argument. = 0.80 X e^{rt} The way I read the problem however was your statement "By 42000 they want X reduced by 20% or X*.80." If that is the case then I would reason as follows. = 0.7029 X units. Penny
