Question

assuming the growth rate stays constant at 1.2%, how many doublings would take place in a 500- year period?

Answer 1

9514 1404 393

Answer:

  8.6

Step-by-step explanation:

The growth factor per year is 1.012, so in 500 years is ...

  1.012^500

The number of doublings is the solution to ...

  2^n = 1.012^500

Taking logarithms, we have ...

  n·log(2) = 500·log(1.012)

  n = 500·log(1.012)/log(2) ≈ 8.6046

About 8.6 doublings will take place in 500 years.