119: Growth and Decay

Last updated about 5 years ago

19 questions

1

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119: Growth and Decay

Last updated about 5 years ago

19 questions

1

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

1

Draggable item		Corresponding Item

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%)

1

What is the percent of increase/decrease?

1

What is the percent of increase/decrease?

1

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

1

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

1

Draggable item		Corresponding Item

1

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

Write the equation to model this situation.

1

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

1

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.

1

How much caffeine will remain after 2 hours?

1

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.

1

How many people were at the last game?

1

Solve your choice from [17]:

0

You can now do the first two sections of DeltaMath.

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

Decay

Growth

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

Draggable item		Corresponding Item
DECAY		b>1
GROWTH		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%)

Is it growth or decay?

Growth

Decay

What is the percent of increase/decrease?

Is it growth or decay?

Growth

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:

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

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

growth

decay

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

An element with mass 670 grams decays by 21.8% per minute. To the nearest tenth, how many grams of the element remain after 15 minutes?

670 dollars is placed in an account with an annual interest rate of 7.82%. How much will be in the account after 26 years, to the nearest cent?

A town has a population of 670 and grows at 21.8% every year. What will be the population after 5 years, to the nearest whole number?

A new TV is purchased for 670 dollars. The value of the TV depreciates at 78.2% per year. What will the value of the car be, to the nearest cent, after 11 years?

Solve your choice from [17]:

Choose all that are true

I am confident in this lesson.

I would like some assistance.

I can distinguish between growth and decay equations.

Given a word problem, and I can write and evaluate a growth or decay situation.

You can now do the first two sections of DeltaMath.

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

Decay

Growth

DECAY

b>1

GROWTH

b<1

Is it growth or decay?

Growth

Decay

Is it growth or decay?

Growth

Decay

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

DECAY

y=a(1+r)^x

GROWTH

y=a(1-r)^x

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

growth

decay

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

An element with mass 670 grams decays by 21.8% per minute. To the nearest tenth, how many grams of the element remain after 15 minutes?

670 dollars is placed in an account with an annual interest rate of 7.82%. How much will be in the account after 26 years, to the nearest cent?

A town has a population of 670 and grows at 21.8% every year. What will be the population after 5 years, to the nearest whole number?

A new TV is purchased for 670 dollars. The value of the TV depreciates at 78.2% per year. What will the value of the car be, to the nearest cent, after 11 years?

Choose all that are true

I am confident in this lesson.

I would like some assistance.

I can distinguish between growth and decay equations.

Given a word problem, and I can write and evaluate a growth or decay situation.

119: Growth and Decay

119: Growth and Decay

Notes L7-1: Exponential Growth & Decay

What is the percent of increase/decrease?

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?

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?

Solve your choice from [17]:

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:

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.