The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.

Question

(a) Estimate how long it takes the population to double. (Round your answer to two decimal places.)

(b) Estimate how long it takes the population to triple. (Round your answer to two decimal places.)

It says using the population growth model.

Thanks for the help!!

Answer 1

Hi Danny L.,

The formula for growth is A(t) = A_oe^kt, where A(t) is the amount at time t, A_o is the initial amount, and k is a positive constant, and e^(x) is the natural exponential function. With A_o = 7.1E9 (7.1 billion) and

k = 0.011 (1.1%):

A(t) = A_oe^kt, given, equation [1]

A(t) = 7.1E9e^0.011t, equation [2]

a) We are asked to find a doubling of the population, or when A(t) = 2A_o. For a doubling (or multiple of A_o) we can write equation [1] as;

A(t) = A_oe^0.011t,

2A_o = A_oe^0.011t, (replace A(t) = 2A_o)

2 = e^0.011t,

ln(2) = ln(e^0.011t),

ln(2) = 0.011t,

ln(2)/0.011 = t

t = 63.01 years, (t is in years)

Notice how we didn't need 7.1 billion to find the doubling.

b) See if you can do the tripling where A(t) = 3A_o.

I hope this helps, Joe.