Question

A culture started with 1,000 bacteria. After 6 hours, it grew to 1,000 bacteria. Predict how many bacteria will be present after 15 hours.
Round your answer to the nearest whole number.
P=Ae^kt

Answer 1

some typo here yes?

Answer 2

start with 1,000 grow to 1,000 means it did not grow at all.

Answer 3

i agree

Answer 4

Sowwy :( it grew to 1,100

Answer 5

P=Ae^kt
what does this signify?

Answer 6

ok it grew by 10% yes?

Answer 7

The formula.
& yes

Answer 8

we have a choice. we can use the stupid formula you wrote, or we can do it an easier way. which do you choose?

Answer 9

okay
A=1000
t=6 hrs
P=1100
1100=1000* e^6k
e^6k=1.1
solve for k

Answer 10

i will let sriram use the formula if desired. but we can do this.
it increases by 10% every 6 hours so i would just write
\[A=1000\times(1.1)^{\frac{t}{6}}\]

Answer 11

using this value of k
P=1000*e^15k
solve for P

Answer 12

then i replace t by 15 and i am done. i get
\[A=1000\times (1.1)^{\frac{15}{6}}=1269\]
finished

Answer 13

we can work out the annoying
\[P=P_0e^{kt}\] if you like but it takes several steps.
first note that when t = 6 you know P = 1100 so write
\[1100=1000e^{6k}\]
divide by 1000 to get
\[1.1=e^{6k}\] now solve for k to get
\[\ln(1.1)=6k\]
\[k=\frac{\ln(1.1)}{6}\]

Answer 14

now use a calculator to get
\[k=0.0158850\]

Answer 15

now go back and write
\[P=1000e^{.0155885t}\] and finally replace t by 15 to get
\[P=1000e^{.05885\times 15}\]
\[=1000e^{0.238275}\]
\[=1269\]

Answer 16

Thank youuuu <3

Answer 17

same answer except first way takes like two seconds and second way is a pain in the log