Sect 8.1 To model exponential growth and decay Section 8.2 To use e as a base and to apply the continuously and compounded interest formulas.

Slides:

Advertisements

Similar presentations

4-1:Exponential Growth and Decay

Advertisements

CONTINUOUSLY COMPOUNDED INTEREST FORMULA amount at the end Principal (amount at start) annual interest rate (as a decimal) time (in years)

What is Interest? Interest is the amount earned on an investment or an account. Annually: A = P(1 + r) t P = principal amount (the initial amount you borrow.

Exponential Functions Functions that have the exponent as the variable.

5.2 exponential functions

Exponential and Logarithmic Functions

Chapter 2 Functions and Graphs

Exponential Functions and their Graphs

Exponents and Properties Recall the definition of a r where r is a rational number: if then for appropriate values of m and n, For example,

MAT 150 Algebra Class #17.

8.2 Day 2 Compound Interest if compounding occurs in different intervals. A = P ( 1 + r/n) nt Examples of Intervals: Annually, Bi-Annually, Quarterly,

7-6 & 7-7 Exponential Functions

Objective: To identify and solve exponential functions.

8-1: Exponential Growth day 2 Objective CA 12: Students know the laws of fractional exponents, understanding exponential functions, and use these functions.

Exponential Functions An exponential function is a function of the form the real constant a is called the base, and the independent variable x may assume.

Copyright © Cengage Learning. All rights reserved. Exponential and Logarithmic Functions.

3 Exponential and Logarithmic Functions

College Algebra Sixth Edition James Stewart Lothar Redlin Saleem Watson.

Exponential Growth Exponential Decay Graph the exponential function given by Example Graph the exponential function given by Solution x y, or f(x)

Thinking Mathematically

8.2 – Properties of Exponential Functions

7.2 Compound Interest and Exponential Growth ©2001 by R. Villar All Rights Reserved.

ACTIVITY 36 Exponential Functions (Section 5.1, pp )

Compound Interest and Exponential Functions

Chapter 2 Functions and Graphs Section 5 Exponential Functions.

Exponential Functions

Chapter 2 Functions and Graphs Section 5 Exponential Functions.

Journal: Write an exponential growth equation using the natural base with a horizontal asymptote of y=-2.

Xy -21/16 1/ xy -25/4 5/ xy -22/9 2/ xy /3 21/9 xy /2 xy

Applications of Logs and Exponentials Section 3-4.

7.1 Exponential Models Honors Algebra II. Exponential Growth: Graph.

EQ: How do exponential functions behave and why?.

7.1 –Exponential Functions An exponential function has the form y = ab x where a does not equal zero and the base b is a positive number other than 1.

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs Digital Lesson.

Exponential Graphs Equations where the variable (x) is the POWER y = ab x – h + k h moves the graph horizontally k moves the graph vertically.

Section 9.3 We have previously worked with exponential expressions, where the exponent was a rational number The expression b x can actually be defined.

a≠0, b>0,b≠1, xєR Exponential Growth Exponential Decay (0,a) b > 1, b = _______________ a = __________________ H. Asymptote: y = ______ 0 < b < 1, b =

Exponential Functions Compound Interest Natural Base (e)

1 Example – Graphs of y = a x In the same coordinate plane, sketch the graph of each function by hand. a. f (x) = 2 x b. g (x) = 4 x Solution: The table.

6.6 The Natural Base, e Warm-up Learning Objective: To evaluate natural exponential and natural logarithmic functions and to model exponential growth and.

Section 6 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Exponential and Logarithmic Equations; Further Applications.

3.1 (part 2) Compound Interest & e Functions I.. Compound Interest: A = P ( 1 + r / n ) nt A = Account balance after time has passed. P = Principal: $

Section 5.7 Compound Interest.

Copyright © 2011 Pearson Education, Inc. Managing Your Money.

7.1 Exploring Exponential Models p434. Repeated multiplication can be represented by an exponential function. It has the general form where ***x has D:

Section 3.1 Exponential Functions. Definition An exponential function is in the form where and.

Slide Copyright © 2012 Pearson Education, Inc.

Math – Solving Problems Involving Interest 1.

11.2 Exponential Functions. General Form Let a be a constant and let x be a variable. Then the general form of an exponential function is:

5.2 Exponential Functions and Graphs. Graphing Calculator Exploration Graph in your calculator and sketch in your notebook: a) b) c) d)

Find the amount after 7 years if $100 is invested at an interest rate of 13% per year if it is a. compounded annually b. compounded quarterly.

Section 6.7 Financial Models. OBJECTIVE 1 A credit union pays interest of 4% per annum compounded quarterly on a certain savings plan. If $2000 is.

Chapter 4.2 Exponential Functions. Exponents and Properties Recall the definition of a r, where r is a rational number: then for appropriate values of.

6.6 Compound Interest. If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed in decimals, the interest.

8.1 Exponential Growth 8.2 Exponential Decay. Exponential Function An exponential function has a positive base other than 1. The general exponential function.

Exponential Growth and Decay. M & M Lab Part 1- Growth What happened to the number of M&Ms? Part 2-Decay What happened to the number of M&Ms? Increased.

Unit 8, Lesson 2 Exponential Functions: Compound Interest.

8.2 Interest Equations Key Q-How is an exponential function used to find interest? These are all money problems so you should have two decimal places.

The Natural Base e An irrational number, symbolized by the letter e, appears as the base in many applied exponential functions. This irrational number.

What do you remember about the following:  1) What is factoring? Give an example.  2) What exponent rules do you remember? Give examples (there are 5).

Section 3.4 Continuous Growth and the Number e. Let’s say you just won $1000 that you would like to invest. You have the choice of three different accounts:

Bellwork Evaluate each expression Solve. for x = bacteria that double 1. every 30 minutes. Find the 2. number of bacteriaafter 3 hours

MAT150 Unit 4-: Exponential Functions Copyright ©2013 Pearson Education, Inc.

Copyright © Cengage Learning. All rights reserved. Exponential and Logarithmic Functions.

Section 8-2 Properties of Exponential Functions. Asymptote Is a line that a graph approaches as x or y increases in absolute value.

Obj: Evaluate and graph exponential functions. Use compound formulas. Warm up 1.Find the limit. x ,00050,000100,000150,000 y.

Algebra II 8-1 (2). Starter: Graph: y = 2(4) x+3 -2 Asymptote: Domain: Range:

Recall the compound interest formula A = P(1 + )nt, where A is the amount, P is the principal, r is the annual interest, n is the number of times the.

Unit 3: Exponential and Logarithmic Functions

Presentation transcript:

Sect 8.1 To model exponential growth and decay Section 8.2 To use e as a base and to apply the continuously and compounded interest formulas

EXPONENTIAL FUNCTIONS where ‘a’ is the beginning value or y-intercept ‘b’ is the base and ‘x’ is the exponent. Characteristics 1)Constant for a base (except 1). 2)Variable for an exponent. 3)Shows increasingly rapid growth when b > 1. 4)Shows increasingly rapid decay when the 0 < b < 1. 5)Horizontal Asymptote at y = 0.

Growth Functions Decay Functions

GRAPH OF THE NATURAL BASE ‘e’ FUNCTION ‘e’ is a constant, irrational number, much like π. The base ‘e’ occurs in many business, financial and engineering applications. ‘e’ ≈ 2.718…….. Graph: Horizontal asymptote is y = 0 xy

Ex 1. Ex. 2 Ex. 3

CONTINUOUS COMPOUND INTEREST This formula is used for continuous or an infinite number of compounds per year. A – Amount (after interest is earned) P – Principal (money initially invested) r – interest rate (percentage written as a decimal) t – time in years

* Ex. 1 Suppose you invest $1300 at an annual interest rate of 4.3% compounded continuously. Find the amount you will have in the account after 3 years. * Ex 2 Suppose you invest $100 at an annual interest rate of 4.8% compounded continuously. Find the amount you will have in the account after 3 years. * Ex 3 Suppose you put $1000 in an account earning 5.5% interest compounded continuously. How much will be in the account after one year? Four years?

COMPOUND INTEREST This formula is used for ‘n’ compounds per year where ‘n’ is a finite number. A – Amount (after interest is earned) P – Principal (money initially invested) r – interest rate (percentage written as a decimal) n – number of compounds per year t – time in years

COMPOUND INTEREST If $12,000 is invested into an account and it earns 9% interest, find the total amount in the account after 5 years if interest is compounded quarterly.

If $1,000 is invested into an account and it earns 8 ½ % interest, find the total amount in the account after 10 years if interest is compounded monthly. How much money would be in the account if interest were compounded continuously?

Suppose you would like to have $100,000 in an account 25 years from now. How much should you invest into an account that pays 12% interest and interest is compounded quarterly?