The world population was 6.7 billion at the beginning of 2008. An exponential model predicts the population to be P(t)=6.7ekt billion t years after 2008, where k is the continuous annual growth rate.
(a) How long does the model predict it will take for the population to reach 10 billion, as a function f(k)?
(b) One current estimate is k = 0.012 = 1.2%. How long will it take for the population to reach 10 billion if k has this value?
(c) For continuous growth rates near 1.2%, find a linear function of k that approximates the time for the world population to reach 10 billion.
(d) Find the time to reach 10 billion and its approximation from part (c) if the continuous growth rate is 1.0%.