The Number of Bacteria in a Culture Is Increasing According $t$

question 81

Multiple Choice

The number of bacteria in a culture is increasing according to the law of exponential growth. After 5 hours there are 175 bacteria in the culture and after 10 hours there are 425 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places.
(i) Find the initial population.
(ii) Write an exponential growth model for the bacteria population. Let $t$ represent time in hours.
(iii) Use the model to determine the number of bacteria after 20 hours.
(iv) After how many hours will the bacteria count be 15,000 ?

• A) (i) \(72.0588\); (ii) \(y = 72.0588 e ^ { 0.1987 t }\); (iii) \(3,819.3668\); (iv) \(32.4162 \mathrm { hr }\)
• B) (i) \(74.2088\); (ii) \(y = 74.2088 e ^ { 0.2338 t }\); (iii) \(5,194.0840\); (iv) \(34.6442 \mathrm { hr }\)
• C) (i) \(72.0588\); (ii) \(y = 72.0588 e ^ { 0.1775 t }\); (iii) \(2,506.6327\); (iv) \(30.0817 \mathrm { hr }\)
• D) (i) \(77.8388\); (ii) \(y = 77.8388 e ^ { 0.2409 t }\);(iii) \(7,945.5374\);(iv) \(36.7554 \mathrm { hr }\)
• E) (i) \(79.3988\); (ii) \(y = 79.3988 e ^ { 0.2598 t }\); (iii) \(10.598 .0009\);(iv) \(38.5348 \mathrm { hr }\)

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