Answer:
a) 4800 bacteria
b) [tex]y(t) = 300(4)^t[/tex]
c) 754 bacteria
Step-by-step explanation:
A bacteria culture starts with 300 bacteria and doubles in size every half hour.
This means that the number of bacteria after t periods of half hour is given by:
[tex]y(t) = 300*(2)^{t}[/tex]
(a) How many bacteria are there after 2 hours?
2 hours is 2*60/30 = 4 periods of 2 hours, so this is y(4).
[tex]y(4) = 300*(2)^{4} = 300*16 = 4800[/tex]
(b) How many bacteria are there after t hours?
It doubles every half hour, so each hour, it is multiplied by 4. Then
[tex]y(t) = 300(4)^t[/tex]
(c) How many bacteria are there after 40 minutes?
40 minutes is 40/30 = 1.33 periods of half hour. So this is y(1.33).
[tex]y(1.33) = 300*(2)^{1.33} = 754[/tex]
