Question 1188722
the bacteria triples every 8 hours.
there are 100 now.
there are 300 in 8 hours.
there are 900 in 16 hours.
there are 2700 in 24 hours.


the growth is exponential.


let x = the rate of growth each hour.


you get 300 = 100 * x^8


divide both sides by 100 to get:


3 = x^8


solve for x to get:


x = 3 ^ (1/8) = 1.14720269.


that's the rate of growth every hour.


in 8 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 8 = 300.


in 16 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 16 = 900.


in 24 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 24 = 2700.


in 22 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 22 = 2051.556351.


that's your solution.


the equation can be graphed as shown below.


<img src = "http://theo.x10hosting.com/2021/121101.jpg" >


coordinate points are in (x,y) format.
x is the number of hours.
y is the number of bacteria.