Problema Solution
A bacterial culture in a petri dish grows at an exponential rate. The petri dish has an area of 256 mm2, and the bacterial culture stops growing when it covers this area. The area in mm2 that the bacteria cover each day is given by the function ƒ(x) = 2x. What is a reasonable domain for this function?
Answer provided by our tutors
If the bacteria growth per day is given by:
f(x) = 2x
after n days there will be (f(x))^n = 2^n x
The maximum area that the bacteria can reach is 256 mm^2 thus
2^n x <= 256
x <= 256/2^n
Thus the reasonable domain is (0, 256/2^n).