Question

A culture started with 4,000 bacteria. After 8 hours, it grew to 4,400 bacteria. Predict how many bacteria will be present after 9 hours. Round your answer to the nearest whole number. P=Ae^kt

Answer 1

snap way
\[\frac{4400}{4000}=1.1\] model as
\[4000\times (1.1)^{\frac{t}{8}}\] at \(t=9\) you get
\[4000\times (1.1)^{\frac{9}{8}}\] or if you prefer
\[4400\times (1.1)^{\frac{1}{8}}\]

Answer 2

otherwise you can do it the annoying way and solve
\[4000e^{8k}=4400\] for \(k\) then write
\[4000e^{9k}=...\]

Answer 3

So the answer would be 4400 *1.1^1/3?

Answer 4

your answer will be less accurate the second way because inevitable you will truncate
\[k=\frac{\ln(1.1)}{8}\]

Answer 5

no not
\[4400(1.1)^{\frac{1}{3}}\] but rather
\[4400(1.1)^{\frac{1}{8}}\]

Answer 6

here it is done the snap way
http://www.wolframalpha.com/input/?i=4400%281.1%29^%281%2F8%29

Answer 7

pita way is to solve
\[4000e^{8k}=4400\] for \(k\) via
\[e^{8k}=1.1\]
\[8k=\ln(1.1)\]
\[k=\frac{\ln(1.1)}{8}=.0119\]
\[P(t)=4000e^{.0119t}\] and then compute
\[P(9)=4000e^{0.119\times 9}\]
http://www.wolframalpha.com/input/?i=4000e^ {.0119*9%29
notice how close they are