I need help with a math question involving functions
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I need help with a math question involving functions

[From: ] [author: ] [Date: 11-09-26] [Hit: ]
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.......
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.
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
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