Question

What model describes the relationship between the amount of bacteria and time, given that the bacteria quadruple every two hours? Linear, Cubic, Quadratic, Exponential

Answer 1

the answer is exponential

Answer 2

This is exponential.  Start with time increments of 1.  If we have 4^x, then the bacteria population triples every hour (x=0 -> 1, x=1 -> 4, x=2 -> 16, etc).  Now, the problem is that is quadruples every two hours.  If you substitute one hour for two, the equation becomes 4^(x/2).  (Now at 2 hours, it is 4, at 4 hours, it is 16, ect).  I am assuming that the population starts at 1, but it doesn't have to.  Let's say the starting population at time 0 is P.  Then, the population at time x would be P*4^(x/2).  You can verify this for any starting population P>=0 and for any time x>=0.