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Ch 6.4 Exponential Growth & Decay Calculus Graphical, Numerical, Algebraic by Finney Demana, Waits, Kennedy

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**Solving by Separation of Variables**

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**Law of Exponential Change**

The differential equation that describes growth is , where k is the growth constant (if positive) or decay constant (if negative). We can solve this equation by separating the variables.

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v

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**Continuously Compounded Interest**

If A0 dollars are invested at a fixed annual rate r (as a decimal) and compounded k times a year, the amount of money present after t years is: If the interest is compounded continuously (or every instant) then the amount of money present after t years is:

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Finding Half Life

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Modeling Growth At the beginning of summer, the population of a hive of hornets is growing at a rate proportional to the population. From a population of 10 on May 1, the number of hornets grows to 50 in thirty days. If the growth continues to follow the same model, how many days after May 1 will the population reach 100?

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Modeling Growth At the beginning of summer, the population of a hive of hornets is growing at a rate proportional to the population. From a population of 10 on May 1, the number of hornets grows to 50 in thirty days. If the growth continues to follow the same model, how many days after May 1 will the population reach 100?

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Using Carbon-14 Dating Scientists who use carbon-14 dating use 5700 years for its half-life. Find the age of a sample in which 10% of the radioactive nuclei originally present have decayed.

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Using Carbon-14 Dating Scientists who use carbon-14 dating use 5700 years for its half-life. Find the age of a sample in which 10% of the radioactive nuclei originally present have decayed.

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**Newton’s Law of Cooling**

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**Newton’s Law of Cooling**

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**Using Newton’s Law of Cooling**

A hard boiled egg at 98ºC is put in a pan under running 18ºC water to cool. After 5 minutes, the egg’s temperature is found to be 38ºC. How much longer will it take the egg to reach 20ºC?

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**Using Newton’s Law of Cooling**

A hard boiled egg at 98ºC is put in a pan under running 18ºC water to cool. After 5 minutes, the egg’s temperature is found to be 38ºC. How much longer will it take the egg to reach 20ºC?

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6.2 Solving Differential Equations Modeling – Refers to finding a differential equation that describes a given physical situation.

6.2 Solving Differential Equations Modeling – Refers to finding a differential equation that describes a given physical situation.

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