MATH 1101 Chapter 5 Review
Topics Covered
Section 5.1 Exponential Growth Functions
Section 5.2 Exponential Decay Functions
Section 5.3 Fitting Exponential Functions to Data
Section 5.4 Logarithmic Functions
Section 5.5 Modeling with Logarithmic Functions
How to get the most out of this review:
1. Watch the video and fill in the packet for the selected section. (Video links can be found at the two web addresses at the top of this page) 2. After each section there are some ‘Practice on your own’ problems. Try and complete them immediately after watching the video. 3. Check your answers with the key on the last page of the packet. 4. Go to office hours or an on-campus tutoring center to clear up any ‘muddy points’.
Section 5.1 Exponential Growth Functions
Exponential Functions A function is called exponential if the variable appears in the exponent with a constant in the base.
Exponential Growth Function Typically take the form �(�) = �� where � and � are constants. • � is the base, a positive number > 1 and often called the growth factor • � is the � intercept and often called the initial value • � is the variable and is in the exponent of �
Growth Factor, � � is the growth factor and constant number greater than 1. Therefore it can be written in the form:
� = 1 + �
Where � is the growth rate. The rate is a percentage in decimal form. An alternative form of the exponential growth function is:
�(�) = �(1 + �)
Linear vs. Exponential Growth If a quantity grows by 4 units every 2 years, this describes a linear relationship where the slope is 4 �����⁄2 ����� = 2 �����/���� If a quantity grows by a factor of 4 units each year, this describes an exponential relationship and the quantity increases 300% each year. 4 = 1 + 3.00
Example 1 On January 1, 2000, $1000 was deposited into an investment account that earns 5% interest compounded annually. Answer the following: (a) Find a model �(�) that gives the amount in the account as a function of �. Let � be the number of years since 2000.
(b) Assuming no withdrawals, how much money will be in the account in 2010?
(c) How long until the account has a balance of $1575?
(d) What year and month did the balance hit $1575?
(e) How long does it take for the account to double in value?
Example 2 How much money must be invested in an account that earns 12% a year to have a balance of $3000 after 4 years? Round your answer to the nearest cent.
How long with it take for the account to double in value?
Finding an exponential function from 2 data points If given two data points for an exponential growth function (0, � ) and (�, � ), you can write the growth formula using the following