How do you write expressions with exponents to help solve problems?
For example, would you rather be paid $4 which doubles daily for four days or accept $50 as total payment for a job?
In this lesson you will learn how to write a numerical expression using
exponents by interpreting a specific problem or situation.
Let’s ReviewLet’s Review
Numerical expressions are mathematical phrases containing
numbers and operations.
13 – (2 x 4)
Let’s ReviewLet’s Review
When finding the value of an
expression, we need to follow the Order of
Operations.
1st P Parentheses2nd E Exponents3rd M Multiply or D Divide from left to right4th A Add or S Subtract from left to right
Let’s ReviewLet’s Review
Exponents tell us how many times to use the base as a factor.
52 = 5 x 5 = 25
Let’s ReviewA Common Mistake
Not reading the problem carefully or misinterpreting the situation.
Not looking at the reasonableness of an answer.
Let’s ReviewCore Lesson Would you rather be paid $4 which doubles daily for four days or accept $50 as total
payment for a job?
What do we know? What do we want to know?
Paid $4 that doubles everyday for 4 days or paid $50 total
Which pays more?
Let’s ReviewCore Lesson
Let’s take a look at our earnings for each day.
Day 1 Day 2 Day 3 Day 4
$4 $4 x 2 $4 x 2 x 2 $4 x 2 x 2 x 2
Let’s ReviewCore Lesson
The numerical expression which would give us the total would be
$4 + ($4 x 2) + ($4 x 22) + ($4 x 23)
$4 + ($4 x 2) + ($4 x 2 x 2) + ($4 x 2 x 2 x 2)
Let’s ReviewCore Lesson
$4 + ($4 x 2) + ($4 x 22) + ($4 x 23)
$4 + ($4 x 2) +
$4 + + + $16 $8 $32
$20 + $40
$60
($4 x 4) + ($4 x 8)
Let’s ReviewCore Lesson
So, which is more profitable? $50 or $4 which doubles each day for 4
days?
In this lesson you have learned how to write a numerical
expression using exponents by interpreting a specific problem.
Let’s ReviewGuided Practice
If you are to be paid $4 which doubles daily each day, how much money would you make on day 10? (Hint: Take a look at the pattern.)
Day Expression $
1 4 4
2 4 • 2 8
3 4 • 22 16
4 4 • 23 32
5
6
7
8
9
10
Let’s ReviewExtension Activities
A population of 50 rabbits triples every two months. Write a numerical expression using exponents that shows what the population of rabbits will be in 6 months.
Let’s ReviewExtension Activities
A population of 50 rabbits triples every two months. Write a numerical expression that could be used to show how many months it would take for there to be over 4000 rabbits.
Let’s ReviewQuick Quiz
A group of 20 bacteria triples in size everyday. What numerical expression shows the number of bacteria on day three?
What numerical expression shows the total number of bacteria at the end of day three?