Exponential and Logarithmic Functions, algebra homework help

Exponential and Logarithmic Functions

Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it.

1. REASONING Use the properties of exponents to prove the Power Property of Logarithms.
2. OPEN ENDED Give an example of a quantity that grows or decays at a fixed rate. Write a real-world problem involving the rate and solve by using logarithms.
3. Writing in Math Use the information about banking on page 556 to explain how the natural base e is used in banking. Include an explanation of how to calculate the value of an account whose interest is compounded continuously, and an explanation of how to use natural logarithms to find the time at which the account will have a specified value in your answer.

Continuously Compounded Interest
2
2.4414.
GET READY for the Lesson
Suppose a bank compounds
interest on accounts continuously,
that is, with no waiting time
between interest payments.
To develop an equation to
determine continuously
compounded interest, examine
what happens to the value A of
an account for increasingly larger
numbers of compounding
periods n. Use a principal P of $1,
an interest rate r of 100% or 1,
and time 1 of 1 year
2.6130
A=P(14″
(yearly)(1+)
(quarterly) 1(+3)
(monthly) (1)
2.7145.
2.7181..
365
(daily
8760
(hourly)
(1)
(1 d.)