Question

How do I show that y = Ce^kt is y=800(9)^t/4 given:
-The initial size of a bacterial culture is 800
-After 4h there are 7200 bacteria

Answer 1

plug in t = 0, that will give you
y = 800 (9^0) = 800*1 =800.
then after 4 hours, so t=4 , plug in that into the original equation. so
y = 800 (9^(4/4))= 800 * 9^1 = 800*9 = 7200

Answer 2

t=0 is the initial size, at the beginning

Answer 3

Where does the 9 come from? I'm not sure if you got the right meaning of the question. The exact question is: The initial size of a bacterial culture is 800. After 4h there are 7200 bactera. By starting with y=Ce^kt, show that the simplified equation is y=800(9)^(t/4). I think what it is saying is put the information it gives you into Ce^kt to get y=800(9)^t/4.

Thanks for replying, I appreciate it :)