1. If you don’t brush your teeth regularly, it won’t take long for large colonies of bacteria to grow in your mouth. Suppose a single bacterium lands on your tooth and starts multiplying by a factor of 4 every hour.
d. After how many hours will there be at least 1,000,000 bacteria in the colony?

Question

1. If you don’t brush your teeth regularly, it won’t take long for large colonies of bacteria to grow in your mouth. Suppose a single bacterium lands on your tooth and starts multiplying by a factor of 4 every hour.
d. After how many hours will there be at least 1,000,000 bacteria in the colony?

deoxna · Answer

The bacteria colony grows by the function:
$$f(h)=4^{h}$$
By the end of h hours there should be 1,00,000 bacteria, so:
$$\ln (1000000)/\ln (4)=h$$
$$h \approx9.97$$
You can now round your answer to say it will take 10 hours, or you could say that it will take 9 hours, 57 and 56.8 seconds approximately :)