A Curve Passes Through the Point $( 8,2 )$ And Has the Property That the Slope of the Curve

question 16

Multiple Choice

A curve passes through the point $( 8,2 )$ and has the property that the slope of the curve at every point $P$ is 3 times the y-coordinate $P$ . What is the equation of the curve?

• A) \(y = 2 e ^ { 3 x + 24 }\)
• B) \(y = \frac { e ^ { 3 x - 24 } } { 2 }\)
• C) \(y = 2 e ^ { 3 x - 8 }\)
• D) \(y = 2 e ^ { 3 x - 24 }\)
• E) \(y = 2 e ^ { x - 24 }\)

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Definitions:

Annual Dividend

The regular payment made by a corporation to its shareholders, often expressed as a fixed amount per share that is distributed annually.

Downsizing Mode

A corporate strategy involving the reduction of a company's size, typically through layoffs, to reduce costs and improve efficiency.

Dividends

The portion of a company's profits distributed to shareholders, typically in the form of cash payments or additional shares.

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A fixed interest rate that does not change throughout the duration of the loan or investment period.