Question

During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 5:00 AM there were 4,000 bacteria present in the culture. At Noon, the number of bacteria grew to 4,600. How many bacteria will there be at midnight?

Answer 1

HI!!

Answer 2

want to do this the easy way?

Answer 3

sure

Answer 4

ok how many hours between 5:00 am and noon?

Answer 5

7

Answer 6

and it grew from 4,000 to 4,600
step one is to do \(\frac{4,600}{4,000}\) and reduce

Answer 7

23/20

Answer 8

ok so we can use
\[P(t)=4,000\left(\frac{23}{20}\right)^{\frac{t}{7}}\]

Answer 9

then figure out how many hours from 5:00 am to midnight, and use that for \(t\)

Answer 10

So, 4000(23/20)^19/7? I got 5845.36

Answer 11

hmm wait a sec

Answer 12

ok looks good let me check the answer

Answer 13

looks good to me
\[\color\magenta\heartsuit\]

Answer 14

Thank you so much!

Answer 15

\[\color\magenta\heartsuit\]