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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Definitions:

Ethernet

A family of computer networking technologies commonly used in local area networks (LAN), metropolitan area networks (MAN), and wide area networks (WAN).

Standard Communications Protocol

A set of rules and standards that allow different systems and devices to communicate with each other effectively.

Client/Server Networks

A network architecture where computers (clients) request services or resources from other computers (servers).

Transmission Media

The radio waves or the physical system (cable) that transports data on a network.