Solve the Problem $P ( t )$ Decreases by Half Every $5 \mathrm { hr }$

question 158

Multiple Choice

Solve the problem.
-Eight million E. coli bacteria are present in a laboratory culture. An antibacterial agent is introduced and the population of bacteria $P ( t )$ decreases by half every $5 \mathrm { hr }$ . The population can be represented by $P ( t ) = 8,000,000 \left( \frac { 1 } { 2 } \right) ^ { t / 5 }$ . Convert this to an exponential function using base $e$ .

• A) \(P ( t ) = 8,000,000 e ^ { - 0.13863 t }\)
• B) \(P ( t ) = 4,000,000 e ^ { - 0.13863 t }\)
• C) \(P ( t ) = 8,000,000 e ^ { - 0.1 t }\)
• D) \(P ( t ) = 4,000,000 e ^ { - 0.1 t }\)

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Definitions:

Economic Impact

The effect of an event, policy, or market condition on the economy, which can be observed in changes to GDP, employment, or investment.

Price Floor

A government-imposed limit on how low a price can be charged for a product, typically above the equilibrium price to help producers.

Quantity Demanded

The total amount of a good or service that consumers are willing to purchase at a given price over a specified period.

Rationing Mechanism

A system or method used to distribute scarce resources or goods among consumers, often based on criteria other than price.