Solve the Problem $x$ Years Can Be Described By $\mathrm { A } ( \mathrm { x } ) = 100 \mathrm { e } ^ { - 0.01569 \mathrm { x } }$

question 17

Multiple Choice

Solve the problem.
-Suppose the amount of a radioactive element remaining in a sample of 100 milligrams after $x$ years can be described by $\mathrm { A } ( \mathrm { x } ) = 100 \mathrm { e } ^ { - 0.01569 \mathrm { x } }$ . How much is remaining after 58 years? Round the answer to the nearest hundredth of a milligram.

• A) \(0.40 \mathrm { mg }\)
• B) \(248.44 \mathrm { mg }\)
• C) \(91.00 \mathrm { mg }\)
• D) \(40.25 \mathrm { mg }\)

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Definitions:

Short Run

A period in economics during which at least one factor of production is fixed, limiting the ability of the economy or firm to adjust.

Long Run

A time frame in economics where all factors of production can be varied, allowing for full adjustment to changes.

Marginal Revenue

The enhanced earnings a business receives by selling one more unit of its goods or services.

Marginal Cost

The swell in overall financial outlay resulting from the crafting of an extra unit of a good or service.