Question

The world’s population is about `f(t)=6.91e^{0.011t}` where `t=0` is year 2010. Find `f(0),f'(0),f(14),f'(14)`?

Answer 1

`f'(t)=.011(6.91)e^{.011t}= 0.07601e^{.011t}` so `f(0)=6.91` and `f'(0)=.076` and `f(14)=6.91e^{.011(14)}=8.06` and `f'(14)=0.07601e^{.011(14)}=0.087`.

This means in 2010 there were 6.91 billion people growing at the rate of 76 million per year. In 2024 there will be 8.06 billion people growing at a rate of 87 million per year.