According to Newton's Law of Heating, the Temperature $T$ Of a Cold Object Increases at a Rate Proportional to a Cold

question 98

Essay

According to Newton's Law of Heating, the temperature $T$ of a cold object increases at a rate proportional to the difference between $T$ and the temperature $T _ { o }$ of its surroundings.(a) Write down this law as a differential equation.(b) Assume the room temperature is 70 $^\circ$ F. If it takes 10 minutes for a can of soda to warm up from 30 $^\circ$ F to 35 $^\circ$ F, and how long it takes to warm up a can of soda from 30 $^\circ$ F to 40 $^\circ$ F.

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Definitions:

Break-Even

Break-even is the point at which total revenues equal total costs, resulting in no net profit or loss, indicating the volume of sales needed to cover costs.

Fixed Expense

Fixed expenses are costs that do not change with the level of production or sales volume, such as rent or salaries.

Target Profit

The target profit a business seeks to reach over a defined timeframe.

Unit Sales

The quantity of items or products sold, not taking into account the selling price or revenue generated.