3 years ago

Please help with 1c, 2, and 3. i would appreciate if you explained what you did step by step :)

Mathematics

1 answer:

Nikitich [7]3 years ago

8 0

1c . 1.55 or 1 11/20

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The population of bacteria in a culture doubles every 14 hours. How long will it take for

Snezhnost [94]

Answer: 22 hours 11 minutes

<u>Step-by-step explanation:</u>

$P=P_o\cdot e^{(kt)}\\\\\text{Since the initial population is doubled in 14 hours, then:}\\2P_o=P_o\cdot e^{k\cdot 14}\\2=e^{14k}\\ln\ 2=ln\ e^{14k}\\ln\ 2=14k\\\\\dfrac{ln\ 2}{14}=k\\\\0.0495=k\\\\\\\text{Now that the k-value has been determined, we can find the time when the}\\\text{population is tripled:}\\3P_o=P_o\cdot e^{0.0495t}\\3=e^{0.0495t}\\ln\ 3=ln\ e^{0.0495t}\\ln\ 3=0.0495t\\\\\dfrac{ln\ 3}{0.0495}=5\\\\22.19=t\\\\22\ hrs +0.19\ hrs$