Question

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.

b. How many bacteria will be in the colony after 7 hours?

Answer 1

This problem is represented by an exponential function of the form..\[a^x\]Since, your growth factor is 4 we substitute that for 'a'.\[4^x\]As 'x' increases, or as time passes, the function increases exponentially. After 7 hours, the function has increased like this:\[4^7=16384\]Therefore, after 7 hours there will be 16384 bacteria in the colony.