Solve the Differential Equation $$4 \frac { d w } { d t } + 9 e ^ { t + w } = 0$$

question 22

Multiple Choice

Solve the differential equation. $$4 \frac { d w } { d t } + 9 e ^ { t + w } = 0$$

• A) \(w = \frac { 9 } { 4 } e ^ { t } - C\)
• B)
• \(w = - \ln \left( \frac { 9 e ^ { t } } { 4 } - C \right)\)
• C)
• \(w = \ln \left( \frac { 4 } { 9 } + \frac { 4 } { 9 } C e ^ { t } \right) - t\)
• D)
• \(w = \ln \left( \frac { 4 } { 9 } t \right) - t\)
• E) none of these

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Definitions:

Concentration Ratio

A measure of the market share controlled by the largest firms within an industry, used to indicate the degree of market competition.

Market Share

The percentage of an industry's sales that a particular company controls.

Herfindahl-Hirschman Index

A measure of market concentration used to determine the level of competition within an industry, calculated by summing the squares of the market shares of all firms in the market.

Marginal Revenue

The additional income that is gained from selling one more unit of a good or service, crucial for businesses when deciding how much to produce.