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A bacteria culture starts with 300 bacteria and grows at a rate proportional to its size. After 3 hours, there are 9000 bacteria
A.) Find an expression for the number of bacteria after t hours. for this part, i got [tex]300*e^{1.133732*t}[/tex]
B.) Find the number of bacteria after 4 hours. well using the expression from above and subbing in 4, i get 27965.04104
C.) Find the growth rate after 4 hours. this just means that i need to solve for k right?
p(t) = 300e^{kt}
p(3) = 300e^{3k} = 9000
solved for k and got 1.133% right?
D.) After how many hours will the population reach 30000
well setting the equation from part A equal to 30000 and solved for t and got 4.319991
i know that at least one of these are wrong, but i can't figure out which one. can someone tell me what I am doing wrong?
A.) Find an expression for the number of bacteria after t hours. for this part, i got [tex]300*e^{1.133732*t}[/tex]
B.) Find the number of bacteria after 4 hours. well using the expression from above and subbing in 4, i get 27965.04104
C.) Find the growth rate after 4 hours. this just means that i need to solve for k right?
p(t) = 300e^{kt}
p(3) = 300e^{3k} = 9000
solved for k and got 1.133% right?
D.) After how many hours will the population reach 30000
well setting the equation from part A equal to 30000 and solved for t and got 4.319991
i know that at least one of these are wrong, but i can't figure out which one. can someone tell me what I am doing wrong?