Page 103 - Algebra 1

Example
4
Evaluating Expressions with Exponents
Evaluate each expression for the given values of the variables.
a. If m = -2 and y = 2.5, what is the value of ym3? SOLUTION
Caution
Since there are no parentheses around ym in the expression ym3, only m is raised to the third power.
ym3
= (2.5)(-2)3 = (2.5)(-8) = -20
Substitute each variable with the given value. Evaluate the exponent.
Multiply.
_a 2 b. If a=3andb=-1,whatisthevalueof2(5-b)?
Substitute each variable with the given value.
Take the opposite of -1.
Perform operations inside the parentheses. Write the fraction in simplest form. Evaluate the exponent.
Multiply.
SO_LUTION a2
5-b 2( _)
32 =2(_ )
5 - (-1) ( 3 )2
=2 5+1 _3 2
=2(6 ) _1 2
=2(2 ) _1
=2(4 ) = _1
2
c. If a = 3, what is the value of ⎪(– a)3⎥? SOLUTION
⎪(-a)3⎥
= ⎪(-3)3⎥
= ⎪(-3)(-3)(-3)⎥ = ⎪-27⎥
= 27
Substitute the variable with the given value. Evaluate the exponent.
Multiply.
Take the absolute value.
Example
5
Application: Investments
A savings account increases as interest accumulates according to the formula Py = 1.04(Py-1), where Py is the principal balance at the end of
y years and Py-1 is the principal balance after y - 1 years. After 6 years, there is a principal balance of $1450.00. How much is the principal balance after 8 years?
88 Saxon Algebra 1