Question

a culture started with 6000 bacteria. After 3 hours, it grew to 7200 bacteria. predict how many bacteria will be present after 19 hours. Round your answer to the nearst whole number


Note:when solving for k, round to four decimal places.

Answer 1

\[P=Ae ^{kt}\]

Answer 2

that the equation given

Answer 3

\[\frac{7200}{6000}=1.2\] i.e. it increases by 20% in three hours
you can model this as
\[6000\times (1.2)^{\frac{t}{3}}\]

Answer 4

i have no idea how you got that

Answer 5

then replace \(t\) by \(19\) and compute
\[6000\times (1.2)^{\frac{19}{3}}\] with a calculator

Answer 6

lets go slow because i only used the numbers you wrote

Answer 7

you start at 6000 right?

Answer 8

so what is the fracton on 1.2

Answer 9

then it grew to 7200 in 3 hours

Answer 10

that is an increase of 20% as \(7200\div 6000=1.2\)

Answer 11

model as
\[\large P(t)=6000\times (1.2)^{\frac{t}{3}}\]

Answer 12

still have no idea do i multiply 6000 and 1.2

Answer 13

to increase a number by 20% you multiply it by \(1.2\)
this increases by 20% every three hours

Answer 14

in three hours it is \(6000\times 1.2=7200\)
in six hours it is \(6000\times 1.2^2\)
in nine hours it is \(6000\times 1.2^3\)

Answer 15

in 19 hours it is
\[\large 6000\times (1.2)^{\frac{19}{3}}\]