SOLUTION: A bacteria culture starts with 800 bacteria. Two hours later there are 1,280 bacteria. Find an exponential model for the size of the culture as a function of time t in hours. f(t)

An exponential model has the form


    N(t) = , 


where "a" is the initial number of bacteria, "b" is the base of the exponential function and t is the time in hours.


In our case,  the initial value is  a = 800; so we can write this equation


    1280 = ,


describing the scene in 2 hours.


From this equation,


    b =  =  = 1.264911.


So, your exponential function is


    N(t) = .     ANSWER


First question is answered.


To answer the second question, substitute t = 48 hours ("2 days") into the formula


    N(24) =  = 63382376.      ANSWER