Do Now Clickulators.

If , then evaluate

a) b) c) d) e)

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60

The length of the larger base of a trapezoid is 10 cm. It has a height of 5 cm and an area of . What is the length of the small base in square centimeters?

a) b) c) d) e)

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Given that , what will be the last digit of .

a) b) c) d) e)

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a) Cannot be determined from given information

Given is an invertible function and solve for : .

a) b) c) d) e)

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Frankie took four tests and got an average score of 87.5%. If his fifth test raised his average to 90%, what was his score on that test?

a) b) c) d) e)

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60

Given that quadrilateral is a square and is equilateral. If determine the distance between and rounded to the nearest meter.

a) b) c) d) e)

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60

𝑃

𝐴 𝐵

𝐶𝐷

ObjectivesCRS

NCP 703: Exhibit knowledge of logarithms and geometric sequences

13.November.2012 Students will be able to…

Evaluate, analyze, and graph exponential functions Solve problems involving exponential growth and

decay.

Exponential Functions Let and

How are and different?

Functions similar in form to are exponential functions

Exponential Functions Which ones are exponential functions?

Graphs of exponential functions

For the parent function: .

Domain: All real numbers

Range:

Growth Versus Decay Exponential

Growth

Exponential Decay

Transformations

𝑒 Most real world applications of involving

exponential growth or decay don’t involve base 2 or 10, but actually an irrational number named

It is derived using calculus to determine the value of the function as .

Applications Compound interest:

A bank account has interest. If Brufus invests $1000, how much will he have after 1 one year if the bank compounds: Annually? Monthly? Daily? Quarterly?

𝐴=𝑃 (1+ 𝑟𝑛 )𝑛𝑡

Annually:

Monthly

Daily

Compounded Continuously

Let ,

Find:

This is what most banks use to calculate interest.

Compound Interest If $1000 is invested in a savings account

earning 8% interest per year and compounded continuously, how much will be in the account at the end of 10 years if there are no other deposits or withdrawals?

Growth and Decay Annual

growth/decay:

If is growth rate, is positive.

If it is a decay rate, is negative

Continuous growth/decay

If is growth rate, is positive.

If it is a decay rate, is negative

Applications Mexico has a population of

approximately 110 million. If Mexico’s population grows at the rate of 1.42% annually, predict its population in 10 and 20 years.

Applications Mexico has a population of

approximately 110 million. If Mexico’s population grows at the rate of 1.42% continuously, predict its population in 10 and 20 years.

Applications In 1980, there were 190.9 cases of

chicken pox. In 2005, there were 32.2 cases of chicken pox. If the rate of chicken pox cases is decreasing exponentially, determine the rate of decrease.

Doubling If you invest in a savings account

offering 3.5% interest compounded continuously, how long until your money doubles?

Practice Pg. 166 #25 Pg. 167 #35

Exit Ticket Pg. 166 #31 Pg. 167 #36