Question

A culture of bacteria started with 3,000 after 2 hours it grew to 3300. How much will grow at 16 hours? Round to nearest whole. P=Ae^kt

Answer 1

if t=0
P=A
ie A=3,000

Answer 2

P=3300
when t=2hours

Answer 3

you still need to find k,

Answer 4

=(

Answer 5

\[P=Ae^{kt}\]\[3300=3000e^{2k}\]\[\frac{3300}{3000}=e^{2k}\]\[11/10=e^{2k}\]\[\ln{11/10}=2k\]\[k=\frac{\ln(\frac{11}{10})}{2} \]

Answer 6

so
\[P(t)=Ae^{kt}\rightarrow P(t)=3000e^{\frac{\ln(11/10)}{2}t}\]
to find P at t=16
\[P(16)=3000e^{\frac{\ln(11/10)}{2}16}\]