Worksheet/Pg. 269/277 Homework

• Pg. 282 #7, 15, 17Pg. 292 #1 – 20 all

• #50 81,920; 2.31x1019 #51 P(t) = 20(2)t

• #52 8.97 months #53 food, health, etc• #57 38.05 days #58 117.48 days• #27 $669.11 #28 $673.43• #29 $674.43 #30 $674.91• #31 $674.93 #41 $4,161.39• #7 $191,278,744,600.00

5.3 Effective Rates and Annuities

• An $86,000 mortgage for 30 years at 12% APR requires monthly payments of $884.61. Suppose you decide to make monthly payments of $1050.00. When would the mortgage loan be completely paid?

• Suppose you make payments of $884.61 for that same $86,000 mortgage for 10 years and then make payments of $1050.00 until the loan is paid. In how many years total will the mortgage be completely paid?

5.3 Effective Rates and Annuities

• Consider a mortgage loan of $80,000 for a 30 year term with interest at 10% APR and monthly payments.– Determine the monthly payments– Suppose one half of the monthly payment was

made every 2 weeks. When would the mortgage loan be completely paid.

5.3 Effective Rates and Annuities

• Sally contributes $80 monthly into an IRA account that earns 6.25% interest. If Sally starts putting money away when she graduates from college (22), how much money will she have when she retires (67)?

• You have saved $2,500 to put down on a car and you can afford to pay $220 for monthly payments. If you are approved for a 5 year loan at 7.5%, how much car can you afford?

5.3 Effective Rates and Annuities

• The half-life of a certain radioactive substance is 21 days and there are 4.62 grams present initially.– Find an algebraic expression for the amount A of

substance remaining as a function of time.– Find a complete graph of the function.– When will there be less than 1 gram of the

substance remaining?

5.4 Logarithmic Functions and Their Properties

Properties•

•

•

•

•

•

•

• loga xa x

log yay x iff x a

log 1a a

log 1 0a

log xa a x

log log loga a ars r s

log log loga a a

rr s

s

log logca ar c r

5.4 Logarithmic Functions and Their Properties

Solve for x: The Nature of Logarithms• Why do we deal with

positive x values when dealing with logs?

• What information do we always know about a log?

3 52 8x 32 18 4x x

3

1log

27x

2log 4 6x

5.4 Logarithmic Functions and Their Properties

Rewrite the following Logarithms

Word Problem!! • Use an algebraic method to

find how long it would take a town with a population of 50,250, increasing continuously at the rate of 3.25% yearly, to reach a population of 301,500.

3 3 3

15log log 2 log

2x x x

532

2 3log

x y

z