5.2 Exponential Functions

and Graphs

Graphing Calculator Exploration

Graph in your calculator and sketch in your notebook:

a)

b)

c)

d)

Exponential Growth: b>1

• b≠1, b>0

• Increasing

• Asymptote: y=0

• Domain: (-∞,∞)

• Range: (0,+∞)

Exponential Decay: 0<b<1

• b≠1, b>0

• Decreasing

• Asymptote: y=0

• Domain: (-∞,∞)

• Range: (0,∞)

Exponential Functions

What happens when a < 0?

Given the function:

The graphs are reflected about the x-axis

Graphing Calculator Exploration

Graph in your calculator, sketch in your notebook and make a table of the ordered pairs for -2 ≤ x ≤ 2.

e)

f)

g)

Exponential Functions

When a>1, the graph of y = bx vertically stretches

When 0>a>1, the graph of y = bx vertically shrinks

Given the function:

How does the value of a affect the graph of y = bx ?

“multiply y’s by a”

y = a•b x–h + k

How do h and k affect the graph of

y = a•bx ?

h causes y = a•bx to shift horizontally h units right if h > 0 or left if h < 0

k causes y = a•bx to shift vertically k units up if k > 0 or down if k < 0

Practice

Graph. Use integer values of x from -2 to 2 in your table. Describe how the graph can be obtained from the graph of the basic exponential function.

Compound Interest

A = the amount of money that you have after a certain number of years

P = the principal (initial quantity of money)

r = percentage rate (change to a decimal)

t = time in years

n = number of times compounded per year

Practice

5) You deposit $5000 into an account, which earns 6% compound interest. Assuming that you do not withdraw any money from the account, after 4 years, how much money will you have…a) if the account is compounded monthly?

b) if the account is compounded quarterly?

c) if the account is compounded daily?

Let’s say that:r=100%P=1t=1

Compound Interest

That yields:

What happens to A as n∞ ?

Natural base, e - the Euler #

Use the e button on your calculator to find e1.35 to four decimal places.

Graph: y = ex

Graph: y = e−x

e ≈ 2.718281828