Question

Bacteria Growth The number N of bacteria in a culture is given by the model N = 100ekt, where t is the time (in hours), with t = 0 corresponding to the time when N = 100. When t = 6, there are 140 bacteria. How long does it take the bacteria population to double in size? To triple in size? 29. Carbon Dating The ratio of carbon 14 to carbon 12 in a piece of wood discovered in a cave is R = 1/814. Estimate the age of the piece of wood. 14 to carbon 12 in a 31. Radioactive Decay What percent of a present amount of radioactive cesium (137Cs) will remain after 100 years? Use the fact that radioactive cesium has a half-life of 30 years.

Answer 1

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Given,

The rate of growth is proportional to the number present.

(

dt

dN

​

)∝N

⇒(

dt

dN

​

)=kN

⇒(

N

dN

​

)=kdt

⇒logN=kt+logC

⇒N=ce

kt

At t=0

N=C=1000

∴N=1000e

kt

At t=1hr

N=2000

∴2000=1000e

k

So N=1000e

0.693t

At t=2.5hr

N=1000e

(0.693×2.5)

N=5654.77.

Step-by-step explanation: