119: Growth and Decay

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Bell Assignment:
Yesterday you explored 401(k)s. Was that an example of exponential growth or exponential decay?

Notes L7-1: Exponential Growth & Decay
The equation for exponential functions is:
y=a(b)^{x}
a is the starting amount
b is the base

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Draggable item		Corresponding Item
GROWTH		b>1
DECAY		b<1

example:
Is y=0.5(1.02)^x growth or decay?

What is the percent of increase or decrease?

(The percent of increase/decrease is how far from 100%)

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Is it growth or decay?

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What is the percent of increase/decrease?

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Is it growth or decay?

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What is the percent of increase/decrease?

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If the percent of increase is 12%, what is the base?

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If the percent of decrease is 12%, what is the base?

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Formally, the equations for exponental growth and decay can be written as:

Draggable item		Corresponding Item
GROWTH		y=a(1+r)^x
DECAY		y=a(1-r)^x

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Teen spending is expected to grow 3.5% annually from $79.7 billion in 2006.

Write the equation to model this situation.

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How many billions is the expected amount of money that teens will spend for the year 2020?

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A cup of black tea contains about 68mg of caffeine. The average teen's body can remove approximately 12.5% of the caffeine from their system per hour.

Write the equation to model this situation.

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How much caffeine will remain after 2 hours?

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The attendance for a basetball team declined at a rate of 5% per game throughout a losing season. 15 games were played and 23,500 people were at the first game.

Write the equation to model this situation.

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How many people were at the last game?

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Is it growth or decay? y=670(0.782)^x

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Which situation could y=670(0.782)^x represent?

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Solve your choice from [17]:

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Choose all that are true

You can now do the first two sections of DeltaMath.

119: Growth and Decay

Bell Assignment:Yesterday you explored 401(k)s. Was that an example of exponential growth or exponential decay?

Bell Assignment:

Notes L7-1: Exponential Growth & Decay

Is it growth or decay?

What is the percent of increase/decrease?

Is it growth or decay?

What is the percent of increase/decrease?

If the percent of increase is 12%, what is the base?

If the percent of decrease is 12%, what is the base?

Formally, the equations for exponental growth and decay can be written as:

Teen spending is expected to grow 3.5% annually from $79.7 billion in 2006. Write the equation to model this situation.

How many billions is the expected amount of money that teens will spend for the year 2020?

A cup of black tea contains about 68mg of caffeine. The average teen's body can remove approximately 12.5% of the caffeine from their system per hour. Write the equation to model this situation.

How much caffeine will remain after 2 hours?

The attendance for a basetball team declined at a rate of 5% per game throughout a losing season. 15 games were played and 23,500 people were at the first game.Write the equation to model this situation.

How many people were at the last game?

Is it growth or decay? y=670(0.782)^x

Which situation could y=670(0.782)^x represent?

Solve your choice from [17]:

Choose all that are true

Bell Assignment:Yesterday you explored 401(k)s. Was that an example of exponential growth or exponential decay?

Bell Assignment:

Notes L7-1: Exponential Growth & Decay

Is it growth or decay?

What is the percent of increase/decrease?

Is it growth or decay?

What is the percent of increase/decrease?

If the percent of increase is 12%, what is the base?

If the percent of decrease is 12%, what is the base?

Formally, the equations for exponental growth and decay can be written as:

Teen spending is expected to grow 3.5% annually from $79.7 billion in 2006. Write the equation to model this situation.

How many billions is the expected amount of money that teens will spend for the year 2020?

A cup of black tea contains about 68mg of caffeine. The average teen's body can remove approximately 12.5% of the caffeine from their system per hour. Write the equation to model this situation.

How much caffeine will remain after 2 hours?

The attendance for a basetball team declined at a rate of 5% per game throughout a losing season. 15 games were played and 23,500 people were at the first game.Write the equation to model this situation.

How many people were at the last game?

Is it growth or decay? y=670(0.782)^x

Which situation could y=670(0.782)^x represent?

Solve your choice from [17]:

Choose all that are true

Bell Assignment:
Yesterday you explored 401(k)s. Was that an example of exponential growth or exponential decay?

Teen spending is expected to grow 3.5% annually from $79.7 billion in 2006.

Write the equation to model this situation.

A cup of black tea contains about 68mg of caffeine. The average teen's body can remove approximately 12.5% of the caffeine from their system per hour.

Write the equation to model this situation.

The attendance for a basetball team declined at a rate of 5% per game throughout a losing season. 15 games were played and 23,500 people were at the first game.

Write the equation to model this situation.

Bell Assignment:
Yesterday you explored 401(k)s. Was that an example of exponential growth or exponential decay?

Teen spending is expected to grow 3.5% annually from $79.7 billion in 2006.

Write the equation to model this situation.

A cup of black tea contains about 68mg of caffeine. The average teen's body can remove approximately 12.5% of the caffeine from their system per hour.

Write the equation to model this situation.

The attendance for a basetball team declined at a rate of 5% per game throughout a losing season. 15 games were played and 23,500 people were at the first game.

Write the equation to model this situation.