⦁suppose that the number of bacteria in a dish increases by 50% every four hours. there are 64 bacteria initially. write a function that describes the number of bacteria after t hours have passed. use your function to find out how many bacteria there will be after 100 hours.

It increases 50% every 4 hours.

Let the initial amount be N

After 4 hours, it increases by 50%, so it becomes 1.5*N
(50% increase is multiplying by a factor of 100% + 50% = 150% = 1.5)

After 4 hours again it will be multiplied by 1.5.

For the t hours, we need to know how many 4 hours are there

= (t/4)

So the increase will be:  1.5 * 1.5* 1.5*......N

The number of 1.5 will be equal to the number of 4 hours in t hours = (t/4)

Function =

After 100 hours, t = 100, N = 64

Amount there will be =   

= (1.5^25) * 64

≈ 1616074.77

Hope this explains it.