When the student is 78​, the world will have a population of about _______ billion.

Question

A student is 16 years old and the world has a population of 6.2

billion. Assuming that the population continues to grow at an annual rate of 1.3​%, predict what the​ world's population will be when the student is 78. Use the approximate doubling time formula.

Answer 1

about 13.9 billion at age 78

A = Pe^rt where P = 6.2, r=0.013, t = 78-16 = 62, rt =0.013(62) = 0.806

A = 6.2e^0.806= 13.88 billion population when the student is 78 years old, 62 years after the population was 6.2 billion use a calculator with a natural log and exponential function

32 = 16e^0.013t

2 = e^0.013t

ln2 = 0.013t

t = ln2/0.013 = about 53.32 years doubling time

population reaches 2 x 6.2 = 12.4 billion in 53.32 years

then it reaches 13.88 billion in 62 years, which is 8.68 years more than doubling time

8.68/53.32 = .1628 or 16.28% of doubling time

6.2 doubled = 12.4

6.2 x 2.1628 = about 13.4 billion