Been at this problem for an hour and I can't seem to solve it. Any takers?
A certain culture of the bacterium Streptococcus A initially has 12 bacteria and is observed to double every 1.5 hours.
Streptococcus A (12,000 × magnification)
(a) Find an exponential model n(t) = n02t/a for the number of bacteria in the culture after t hours.
n(t) =
(b) Estimate the number of bacteria after 22 hours. (Round your answer to the nearest whole number.)
bacteria
(c) When will the bacteria count reach 10,000? (Round your answer to one decimal place.)
t = h
Best Answer
EDIT: sorry, I read it as doubling every hour instead of every hour and a half. You would have to replace all of my $2^t$ with $2^{\frac{t}{1.5}}$.
BELOW IS WRONG, SEE NOTE ABOVE
So after t hours there will be $$n(t)=12\cdot 2^t$$ bacteria because it will have doubled t times. Therefore $$n(22)=12\cdot 2^{22}$$ and it will reach 10,000 when $$n(t)=12\cdot 2^t=10000$$ which becomes $$t=\frac{\ln{\frac{10000}{12}}}{\ln{2}}$$