If a bacteria population begins with 300 cells and doubles every 4 hrs, then the number of bacteria after t hours is n= f(t) = 300(2^t/4)
(a) what is the inverse of this function and explain its meaning.
(b) When will the colony reach 30000 cells?
Can someone explain how to answer this question?
(a) what is the inverse of this function and explain its meaning.
(b) When will the colony reach 30000 cells?
Can someone explain how to answer this question?
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a.
f(t) = 300*2^(t/4). Let t = f_inverse (t) = f^(-1) [t]
Then
t = 300*2^(f^(-1)[t]/4).
t/300 = 2^(f^(-1)[t]/4)
log_2 (t/300) = f^(-1)[t]/4
4log_2 (t/300) = f^(-1) [t].
This is the amount of time (in hours) needed to get to a certain number of cells.
b. 4log_2(100) = 8log_2(10) = 8/log(2) = 26.57 hours
f(t) = 300*2^(t/4). Let t = f_inverse (t) = f^(-1) [t]
Then
t = 300*2^(f^(-1)[t]/4).
t/300 = 2^(f^(-1)[t]/4)
log_2 (t/300) = f^(-1)[t]/4
4log_2 (t/300) = f^(-1) [t].
This is the amount of time (in hours) needed to get to a certain number of cells.
b. 4log_2(100) = 8log_2(10) = 8/log(2) = 26.57 hours