Exponential Functions
What is the general formula for an exponential function?
Y=abx
Adding + c in f(x)= 2x + c moves the graph in what direction?
Vertically up
Which grows faster: 2x or 3x?
3x
A population of rabbits starts at 120 and triples every year. Write the exponential growth model and find the population after 12 years.
63,772,920 rabbits
What is the name of the app where people post 10-second videos that often start trends?
Tik Tok
In y=3(2)2, What does "3" represent?
Initial Value
Subtracting d in f(x)=2(x-d) moves the graph in which direction
Horizontally right
Which decays faster: (0.5)x or (0.2)x?
0.2x
A new car costs $30,000 and loses 18% of its value each year. Write the exponential decay model and find its value after 5 years.
11,122.2 dollars
What is Taylor Swift last album?
The life of a show girl
If b>1, what type of exponential function do we have?
Exponential Growth
What transformation occurs if we multiply by a negative outside the exponent?
Reflection across the x-axis.
If a bacteria doubles every hour, what is its growth factor?
2
You invest $1,500 at 6% annual interest compounded quarterly. How much will you have after 10 years?
$2,721.03
What is 50 + 17?
67
What is the horizontal asymptote of f(x)=2x +4?
y=4
What transformation occurs if we make the exponent negative, like 2-x
Reflection across the y-axis.
If a function halves every hour, what is its growth factor?
0.5
Hugo deposits $800 in a savings account that earns 5% interest compounded continuously. How much money will he have after 2 years?
$884.14
What is the name of the streaming service that features shows like Stranger Things and Wednesday?
Netflix
When a is negative in f(x)=a⋅bx what transformation occurs?
Reflection across the x-axis
Describe all transformations from f(x)=2x to f(x)=3*2(x+2) -4
Stretched vertically by 3, shifted left 2, down 4
Explain how exponential growth and decay differ in terms of the base value.
Growth occurs when b>1; decay when 0<b<1
You have 10 donuts and eat half every hour while studying. How many donuts (or crumbs) remain after 5 hours
0.3125 donuts — just sprinkles left!
What is the name of the wizarding school Harry Potter attended?
Hogwarts