U2D3 Exponential Growth and Decay Functions Jan27
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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 ?
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Which option would you choose?
Is this a Growth or Decay Problem?
Example
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.
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.
Determine whether the model represents exponential growth or exponential decay.
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.
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.
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).
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.
