Since we're interested in doubling, let's start with
p(t) = 6.0*2^(kt)
Now we know that p(10) = 6.9, so
6.0*2^(10k) = 6.9
2^(10k) = (6.9/6.0) = 1.15
10k = log1.15/log2
k = 0.02
So, p(t) = 6.0*2^(t/50)
The doubling time is 50 years
If you insist on using base e, then that would be 6.0e^(ln2/50 t)
dp/dt = 6.0 * ln2 * 1/50 * 2^(t/50) = 0.083*2^(t/50)
at t=15, that is 0.102
Given that the population of the earth was 6.0 billion people in 1999 (t = 0) and 6.9 billion people in 2009 (t = 10), find: a) an exponential growth function for the world’s population that fits that two data points. b) Find the doubling time for the world population using the model in part a). c) Find the instantaneous growth rate of the population in 2014 (t = 15).
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