A Curve Passes Through the Point $( 6,2 )$ And Has the Property That the Slope of the Curve

question 82

Multiple Choice

A curve passes through the point $( 6,2 )$ and has the property that the slope of the curve at every point $P$ is 4 times the $\mathrm { y }$ -coordinate $P$ . What is the equation of the curve?

• A) \(y = 2 e ^ { 4 x - 6 }\)
• B) \(y = 2 e ^ { x - 24 }\)
• C) \(y = 2 e ^ { 4 x + 24 }\)
• D) \(y = \frac { e ^ { 4 x - 24 } } { 2 }\)
• E) \(y = 2 e ^ { 4 x - 24 }\)

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Definitions:

Anaerobic Respiration

A form of cellular respiration that occurs without oxygen, producing energy and lactic acid or ethanol.

Creatine Phosphate

An energy storage molecule in muscles that helps rapidly regenerate ATP during high-intensity, short-duration exercises.

Aerobic Respiration

The metabolic process of breaking down substrates with oxygen to produce ATP, carbon dioxide, and water as by-products, occurring in mitochondria.

Isotonic Contraction

A type of muscle contraction in which the muscle changes length while the tension remains constant, usually resulting in movement.