a country's population in 1995 was 164 million. In 2001, it was 169 million. Estimate the population in 2015 using the exponential growth formula. round your answer to the nearest million.

Question

anonymous · Answer

formula for exponential growth is:
$$x_{t}=x_{o}(1+r)^{t}$$
where t is your time (years in this case), r is your rate of growth, xo is your original population, and xt is your population after time t.

Since you have two times with corresponding populations you need to find r first.
xo=164, xt = 169, and the time between is t = 6.  Solve r:
$$r=(169/164)^{(1/6)}-1$$
$$r=(0.005017929)$$

Now that we have r we can sub it back into the equation but change the xt to correspond to the value in  2015. use any of the other populations for xo but adjust the t value accordingly:
$$x_{t}=169(1+0.005017929)^{14}$$ use the values from 2001, which leaves 14 years until 2015, solve:

$$x_{t}=181.26$$