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?