$\text { Solve the differential equation } \frac { d y } { d x } = \left( e ^ { x } + 8 \right) ^ { 2 } \text {. }$

question 34

Multiple Choice

$\text { Solve the differential equation } \frac { d y } { d x } = \left( e ^ { x } + 8 \right) ^ { 2 } \text {. }$

• A) \(y = e ^ { 2 x } + 8 e ^ { x } + 64 x + C\)
• B) \(y = \frac { 1 } { 2 } e ^ { 2 x } + 16 e ^ { x } + 64 x + C\)
• C) \(y = e ^ { 2 x } + 64 e ^ { x } + 16 x + C\)
• D) \(y = \frac { 1 } { 2 } x e ^ { 2 x } + 16 e ^ { x } + 8 x + C\)
• E) \(y = \frac { 1 } { 2 } x e ^ { 2 x } + 8 e ^ { x } + 64 x + C\)

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Definitions:

Elastic Demand

A market scenario where the quantity demanded of a product or service significantly changes in response to a change in price.

Fast-Food

Quick service restaurants serving food that is prepared and served rapidly.

Consumer Surplus

The benefit obtained by consumers because they are able to purchase a product for a price that is less than the highest price that they would be willing to pay.

Optimal Consumption

refers to the situation in which a consumer allocates their income in a way that maximizes their overall satisfaction or utility, given their preferences and the prices of goods and services.