Solve the Exponential Equation Algebraically $1000 e ^ { - 4 x } = 75$

question 7

Multiple Choice

Solve the exponential equation algebraically.Approximate the result to three decimal places. $1000 e ^ { - 4 x } = 75$

• A) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 2.648\)
• B) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 1.352\)
• C) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 1.648\)
• D) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 0.648\)
• E) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 0.352\)

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Definitions:

Natural Monopoly

An industry in which economies of scale are so great that a single firm can produce the industry’s product at a lower average total cost than would be possible if more than one firm produced the product.

Horizontal Market

A market that appeals to a wide range of consumers across different industries or sectors.

Contestable Market

A market with no barriers to entry or exit, where a company's prices and output are constrained by the threat of new entrants or competition rather than by existing competitors alone.

Public Interest Theory

A theory suggesting that regulations are created in response to the public's demand for fair and efficient markets.