, Learning goals for unit 2
• Identify and describe key features of exponential and logarithmic functions
• Make connections between the numerical, graphical, and algebraic representations of logarithmic functions.
• Understand the relationship between exponential and logarithmic expressions
• Evaluate logarithms and apply them to simplify numeric expressions
• Solve exponential and logarithmic equations in one variable algebraically including those in problems arising from
real – world applications.
, Defining logarithmic functions 2 1
.
Exponential functions y a(b)x
=
y = future value
a = initial value
b = 1 + growth rate
X = number of times it has grown
Example 1
in a sample, there were 50 bacteria & now there are 204,800. How many times has the population doubled?
y =
204 ,
800
9 =
50
b =
2 (since its doubling
X = C
204 800 ,
= 50(2)x
Step 1: determine value of x:
X
204 , 800 50(2)
-
50 50
4, 096 = 2x Since 4,096 can be written as a power of 2 we can evaluate this: 21 = 2x
↑
o The population has been doubled 12 times The bases are the same
Therefore x=12
Example 2 y = a(b)x
6 10
Remember 2 = 64 & 2 = 1024
Michelle put $ 800 in a savings account that pays 35 interest compounded annually. How long
will it take for the investment to triple in value ?
Given :
a= $800
y
= 2400(800x3)
b) =
1 035
.
(add 100% and 3 5 %.
.
Then write value as decimal
*
2400 =
800 (1 039) .
*
2400 =
800(1 035)
.
800 800
3 =
1 .
0354
Determinex through trial & error X = 32
It will take approx. 32 years for the investment 2 triple with this rate in interest
What we learn
In this unit we will learn that logarithms can help us efficiently/ accurately determine the value of an unknown exponent
We will appreciate the power of logarithms
• Identify and describe key features of exponential and logarithmic functions
• Make connections between the numerical, graphical, and algebraic representations of logarithmic functions.
• Understand the relationship between exponential and logarithmic expressions
• Evaluate logarithms and apply them to simplify numeric expressions
• Solve exponential and logarithmic equations in one variable algebraically including those in problems arising from
real – world applications.
, Defining logarithmic functions 2 1
.
Exponential functions y a(b)x
=
y = future value
a = initial value
b = 1 + growth rate
X = number of times it has grown
Example 1
in a sample, there were 50 bacteria & now there are 204,800. How many times has the population doubled?
y =
204 ,
800
9 =
50
b =
2 (since its doubling
X = C
204 800 ,
= 50(2)x
Step 1: determine value of x:
X
204 , 800 50(2)
-
50 50
4, 096 = 2x Since 4,096 can be written as a power of 2 we can evaluate this: 21 = 2x
↑
o The population has been doubled 12 times The bases are the same
Therefore x=12
Example 2 y = a(b)x
6 10
Remember 2 = 64 & 2 = 1024
Michelle put $ 800 in a savings account that pays 35 interest compounded annually. How long
will it take for the investment to triple in value ?
Given :
a= $800
y
= 2400(800x3)
b) =
1 035
.
(add 100% and 3 5 %.
.
Then write value as decimal
*
2400 =
800 (1 039) .
*
2400 =
800(1 035)
.
800 800
3 =
1 .
0354
Determinex through trial & error X = 32
It will take approx. 32 years for the investment 2 triple with this rate in interest
What we learn
In this unit we will learn that logarithms can help us efficiently/ accurately determine the value of an unknown exponent
We will appreciate the power of logarithms
