Question

A medical student studying the growth of bacteria in a certain culture has compiled the following data:

number of minutes 0 20
number of bacteria 6000 9000

Use these data to find an exponential function of the form Q(t) = Q0e^kt expressing the number of bacteria in the culture as a function of time.How many bacteria are present after 1 hour?

Answer 1

like finding the equation of a line given two points
with a slight difference

Answer 2

you know it is going to look like
\[Q(t)=Q_0\times e^{kt}\] and you have \(Q_0=6000\)

Answer 3

therefore it is
\[Q(t)=6000e^{kt}\] and all you need is \(k\)

Answer 4

you know if \(t=20\) then \(Q(t)=Q(20)=9000=6000e^{20k}\) set
\[9000=6000e^{20k}\] and solve for \(k\)

Answer 5

first step is to divide by 6000 to get
\[1.5=e^{20k}\]
then
\[\ln(1.5)=20k\] so
\[k=\frac{\ln(1.5)}{20}\]

Answer 6

Q(t)=6000e^(0.203)(t)
so this is my equation?