Pre Cal

Exponential Functions

100

What is the general formula for an exponential function?

Y=ab^x

200

In y=3(2)^2, What does "3" represent?

Initial Value

300

If b>1, what type of exponential function do we have?

Exponential Growth

400

What is the horizontal asymptote of f(x)=2^x +4?

y=4

500

When a is negative in f(x)=a⋅b^x what transformation occurs?

Reflection across the x-axis

Transformations of Exponential Functions

100

Adding + c in f(x)= 2^x + c moves the graph in what direction?

Vertically up

200

Subtracting d in f(x)=2^(x-d) moves the graph in which direction

Horizontally right

300

What transformation occurs if we multiply by a negative outside the exponent?

Reflection across the x-axis.

400

What transformation occurs if we make the exponent negative, like 2^-x

Reflection across the y-axis.

500

Describe all transformations from f(x)=2^x to f(x)=3*2^(x+2) -4

Stretched vertically by 3, shifted left 2, down 4

Comparing Growth & Decay

100

Which grows faster: 2^x or 3^x?

3^x

200

Which decays faster: (0.5)^x or (0.2)^x?

0.2^x

300

If a bacteria doubles every hour, what is its growth factor?

2

400

If a function halves every hour, what is its growth factor?

0.5

500

Explain how exponential growth and decay differ in terms of the base value.

Growth occurs when b>1; decay when 0<b<1

Modeling

100

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

200

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

300

You invest $1,500 at 6% annual interest compounded quarterly. How much will you have after 10 years?

$2,721.03

400

Hugo deposits $800 in a savings account that earns 5% interest compounded continuously. How much money will he have after 2 years?

$884.14

500

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!

Random

100

What is the name of the app where people post 10-second videos that often start trends?

Tik Tok

200

What is Taylor Swift last album?

The life of a show girl

300

What is 50 + 17?

67

400

What is the name of the streaming service that features shows like Stranger Things and Wednesday?

Netflix

500

What is the name of the wizarding school Harry Potter attended?

Hogwarts