U2D3 Exponential Growth and Decay Functions Jan27

Instructions

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Sketch the graph of:

Don't forget all the important features!

1

What is the y-intercept for y = 2x - 1?

1

1

Sketch the graph of:

Don't forget all the important features!

1

What is the y-intercept for y = -2x ?

1

1

Sketch the graph of:

Don't forget all the important features!

1

What is the y-intercept for y = 2x + 5 ?

1

1

Sketch the graph of:

Don't forget all the important features!

1

What is the y-intercept for y = 2-x - 3 ?

1

Draggable item		Corresponding Item

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Which option would you choose?

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Is this a Growth or Decay Problem?

Example

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Growth/Decay Problems - Step-By-Step

A town has a population of 9000 and grows at 3% every year.  What will be the population after 9 years, to the nearest whole number?


a (initial amount) = _______ 
b (growth) = 1 + .% = _______ 
t (time) = _______ 

Write the expression to evaluate.
y = _______ = _______ 

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Write your answers in simplest form.
a. The expression is  _______  when x = -2.
b. The expression is  _______  when x = 3.

1

Write your answers in simplest form.
a. The expression is _______  when x = -2
b. The expression is _______  when x = 3.

1

Write your answers in simplest form.
a. The expression is _______  when x = -2.
b. The expression is _______  when x = 3.

1

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

1

Identify the graph of the function.
What do get when you plug 1 in for x?
Try not to use technology.

1

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

MODELING REAL LIFE  
The population P (in millions) of Peru during a recent decade can be approximated by 


where t is the number of years since the beginning of the decade.

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Identify the annual percent increase or decrease in population.

Based on the function, Peru had a _______ % _______ [write "increase" or "decrease"] in population since the beginning of the decade.

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Use the function to estimate the population of Peru 15 years from the beginning of the decade.

The population of Peru was approximately  _______  millions of people. (Round to the nearest hundredths.)

MODELING REAL LIFE
In January of 2012, there were about 6.26​ billion cell phone subscribers in the world. During the next 10 years, the number of cell phone subscribers increased by about 4% each year.

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Write an exponential model that represents the number of cell phone subscribers y​ (in billions) in t​ years after 2012.

y = _______ 

Complete the equation above.

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Use your model to estimate the number of cell phone subscribers in 2016. Round your answer to two decimal places.

There were about _______  billion subscribers in 2016. 
(Round your answer to the nearest hundredths.)

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MODELING REAL LIFE
In January 2024, a social media site had 14.3 million members. The number of members is decreasing by about 8% per year.

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Write an exponential model that represents the number of social media members y​ (in millions) in t​ years after 2024.

y = _______ 

Complete the equation above.

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Use your model to estimate the number of predicted social media members in 2027. 

There will be approximately _______  million members in 2027. 
(Round your answer to the nearest hundredths.)

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MODELING REAL LIFE 
When a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. 
The amount  y​  (in grams) of carbon-14 in the body of an organism  t​  years after the organism dies is 


where  a​  is the initial amount (in grams). 

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What percent of the carbon-14 is released each year? Round your answer to the nearest tenth.

About _______ % of carbon-14 is released each year.

MODELING REAL LIFE 
The number y​ of Salmonella cells on an egg after t​ minutes can be modeled by the equation:


where  a​  is the initial number of cells. 

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By what percent does the number of Salmonella cells increase each minute?

According to the equation, Salmonella increases by _______ % every minute.

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If we started with 20 Salmonella cells, how many would we have after 1 hour?

According to the model, we would have approximately _______  Salmonella cells on an egg after 1 hour. 
(Round your answer to the nearest tenth.)

U2D3 Exponential Growth and Decay Functions Jan27

Sketch the graph of:

Don't forget all the important features!

What is the y-intercept for y = 2x - 1?

Sketch the graph of:

Don't forget all the important features!

What is the y-intercept for y = -2x ?

Sketch the graph of:

Don't forget all the important features!

What is the y-intercept for y = 2x + 5 ?

Sketch the graph of:

Don't forget all the important features!

What is the y-intercept for y = 2-x - 3 ?

Which option would you choose?

Is this a Growth or Decay Problem?

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

Identify the graph of the function.
What do get when you plug 1 in for x?
Try not to use technology.

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

Sketch the graph of:

Don't forget all the important features!

What is the y-intercept for y = 2x - 1?

What is the x-intercept for y = 2x - 1?

Sketch the graph of:

Don't forget all the important features!

What is the y-intercept for y = -2x ?

What is the x-intercept for y = -2x ?

Sketch the graph of:

Don't forget all the important features!

What is the y-intercept for y = 2x + 5 ?

What is the x-intercept for y = 2x + 5 ?

Sketch the graph of:

Don't forget all the important features!

What is the y-intercept for y = 2-x - 3 ?

What is the x-intercept for y = 2-x - 3 ?

Which option would you choose?

Is this a Growth or Decay Problem?

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

Identify the graph of the function.
What do get when you plug 1 in for x?
Try not to use technology.

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

Determine whether the model represents exponential growth or exponential decay.

What is the x-intercept for y = 2x - 1?

What is the x-intercept for y = -2x ?

What is the x-intercept for y = 2x + 5 ?

What is the x-intercept for y = 2-x - 3 ?

Determine whether the model represents exponential growth or exponential decay.

U2D3 Exponential Growth and Decay Functions Jan27

U2D3 Exponential Growth and Decay Functions Jan27

Sketch the graph of:Don't forget all the important features!

What is the y-intercept for y = 2x - 1?

Sketch the graph of:Don't forget all the important features!

What is the y-intercept for y = -2x ?

Sketch the graph of:Don't forget all the important features!

What is the y-intercept for y = 2x + 5 ?

Sketch the graph of:Don't forget all the important features!

What is the y-intercept for y = 2-x - 3 ?

Which option would you choose?

Is this a Growth or Decay Problem?

Identify the graph of the function.What do get when you plug 1 in for x?Try not to use technology.

Identify the graph of the function.What do get when you plug 1 in for x?Try not to use technology.

Identify the graph of the function.What do get when you plug 1 in for x?Try not to use technology.

Sketch the graph of:Don't forget all the important features!

What is the y-intercept for y = 2x - 1?

What is the x-intercept for y = 2x - 1?

Sketch the graph of:Don't forget all the important features!

What is the y-intercept for y = -2x ?

What is the x-intercept for y = -2x ?

Sketch the graph of:Don't forget all the important features!

What is the y-intercept for y = 2x + 5 ?

What is the x-intercept for y = 2x + 5 ?

Sketch the graph of:Don't forget all the important features!

What is the y-intercept for y = 2-x - 3 ?

What is the x-intercept for y = 2-x - 3 ?

Which option would you choose?

Is this a Growth or Decay Problem?

Identify the graph of the function.What do get when you plug 1 in for x?Try not to use technology.

Identify the graph of the function.What do get when you plug 1 in for x?Try not to use technology.

Identify the graph of the function.What do get when you plug 1 in for x?Try not to use technology.

Determine whether the model represents exponential growth or exponential decay.

What is the x-intercept for y = 2x - 1?

What is the x-intercept for y = -2x ?

What is the x-intercept for y = 2x + 5 ?

What is the x-intercept for y = 2-x - 3 ?

Determine whether the model represents exponential growth or exponential decay.

Sketch the graph of:

Don't forget all the important features!

Sketch the graph of:

Don't forget all the important features!

Sketch the graph of:

Don't forget all the important features!

Sketch the graph of:

Don't forget all the important features!

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

Identify the graph of the function.
What do get when you plug 1 in for x?
Try not to use technology.

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

Sketch the graph of:

Don't forget all the important features!

Sketch the graph of:

Don't forget all the important features!

Sketch the graph of:

Don't forget all the important features!

Sketch the graph of:

Don't forget all the important features!

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.

Identify the graph of the function.
What do get when you plug 1 in for x?
Try not to use technology.

Identify the graph of the function.

What do get when you plug 1 in for x?
Try not to use technology.