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U2D3 Exponential Growth and Decay Functions Jan27

Last updated 7 months ago
39 questions
Note from the author:


1

Sketch the graph of:


Don't forget all the important features!

1

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

1

What is the x-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 ?

1

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



1

Sketch the graph of:


Don't forget all the important features!

1

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

1

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



1

Sketch the graph of:


Don't forget all the important features!

1

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

1

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

1
Draggable itemCorresponding Item
1

Which option would you choose?






1

Is this a Growth or Decay Problem?

Example
1
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 = _______ = _______
1
Growth/Decay Problems - Step-By-Step

A town has a population of 18000 and grows at 2% every year. What will be the population after 11 years, to the nearest whole number?


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

Write the expression to evaluate.
y = _______ = _______
1
Growth/Decay Problems - Step-By-Step

A new car is purchased for 17900 dollars. The value of the car depreciates at 12.25% per year. What will the value of the car be, to the nearest cent, after 10 years?


a (initial amount) = _______
b (decay) = 1 - .% = _______
t (time) = _______

Write the expression to evaluate.
y = _______ = _______
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
Write your answers in simplest form.
a. The expression is _______ when x = -2.
b. The expression is _______ when x = 3.
1

1

Identify the graph of the function.

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

1

1

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

1

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.
1

Determine whether the model represents exponential growth or exponential decay.

1
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.
1
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.

1
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.
1
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.)
1
Use your model to estimate when the number of cell phone subscribers will be about 8 billion.

There will be 8 billion cell phone subscribers approximately _______ years and _______ months from January 2012.
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.


1
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.
1
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.)
1
Use your model to predict when the number of social media members will be below 10 million.

There will be 10 million or less social media members approximately _______ years and _______ months from January 2024.
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).
1
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.
1
By what percent does the number of Salmonella cells increase each minute?

According to the equation, Salmonella increases by _______ % every minute.
1
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.)