Aculture contains 1500 bacteria initially and doubles every 30 mins. a) find a function that models the number of bacteria at time t. b) find the number of bacteria after 2 hours. c) after how much time will there be 4000 bacteria

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Below are the answers:

a. An = Ao • 2^(t/30) 
b. An = 1500 • 2^(60*2/30) or An = 24000 
c. 4000 = 1500 • 2^(t/30) 
or 4000/1500 = 2^(t/30) 
or ln(40/15) = (t/30) ln(2) 
or t = 30* ln(8/3) / ln(2) 
or t ~ 42.45 min