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Exponential and Logarithmic FunctionsPowerPoint Presentation

Exponential and Logarithmic Functions

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### ExponentialandLogarithmic Functions

By: Hendrik Pical to Revition

Exponential and Logarithmic Functions

Last Updated: January 30, 2011

With your Graphing Calculatorgraph each of the following

y = 2x

y = 3x

y = 5x

y = 1x

Determine what is happening when the base is changing in each of these graphs.

y = 2x

y = 5x

y = 2xy = 4x

y = 10x

y = (3/2)x

Determine where each of the following would lie?

y=10x

y=4x

y = (3/2)x

y = 1x

Compound Interest

You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded quarterly?

A = Final amount = unknown

P = Principal = $5000

r = rate of interest = .045

n = number of times compounded per year = 4

t = number of years compounded = 10

Compound Interest

You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded quarterly?

A = unknown

P = $5000

r = .045

n = 4

t = 10

Compound Interest

You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded quarterly?

weekly?

A = unknown

P = $5000

r = .045

52

n = 4

t = 10

DECAY

With your Graphing Calculatorgraph each of the following

y = (1/2)x

y = (1/3)x

y = 1x

Determine what is happening when the base is changing in each of these graphs.

A new Number

We could use a spreadsheet to determine an approximation.

Compound Interest-continuously

You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded continuously?

A = Final amount = unknown

P = Principal = $5000

r = rate of interest = .045

t = number of years compounded = 10

Compound Interest-continuously

You deposit $5000 into an account that pays 4.5 % interest. What is the balance of the account after 10 years if the interest is compounded continuously?

A = unknown

P = $5000

r = .045

t = 10

Bacteria Growth

You have 150 bacteria in a dish. It the constant of growth is 1.567 when t is measured in hours. How many bacteria will you have in 7 hours?

y = Final amount = unknown

n = initial amount = 150

k = constant of growth = 1.567

t = time = 7

Bacteria Growth

You have 150 bacteria in a dish. It the constant of growth is 1.567 when t is measured in hours. How many bacteria will you have in 7 hours?

y = unknown

n = 150

k = 1.567

t = 7

logarithmic

x = (½)y

y = log½x

Change of Base Formula

if b = 10

Properties of Logarithms

- Product Property
- Quotient Property
- Power Property
- Property of Equality

Solve for x

checks!

Solve for x

Solution

Solve for n

checks!

Solve for n

Solution

Solve for x

Solution

Solve for x

Solution

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