**8th Grade Students**

## Exponential Functions and Equations

*I will be entering participation grades into PowerSchool and emailing those students with missing assignments*

*Big Ideas Textbook/Khan Academy/i-Ready*

**Solutions to problems 6 – 15, page 289, textbook**

6) linear; As x increases by 1, y increases by 2

7) exponential; as x increases by 1, y is multiplied by 2

8) exponential; as x increases by 1, y is multiplied by 4

9) linear; as x increases by 3, y decreases by 9

10) 9; 11) 1.5 12) -100 13) 8 14) 72 15) 2

**New Assignment (look at the Background Notes below before viewing the videos)**

Back to Khan Academy (Algebra I, Exponential Growth and Decay)

I have assigned the following videos and problem sets from the section Exponential Expressions, to be completed by high noon Friday, March 20.

Video: Exponential Expressions Word problems (numerical); (4 minutes)

Practice: Exponential Expressions Word problems (numerical); (4 problems)

Video: Initial Value and Common Ratio of exponential functions; (5 minutes)

Video: Exponential Expressions Word Problems (algebraic); (3 minutes)

Practice: Exponential Expressions Word Problems (algebraic); (4 questions)

Video: Interpreting exponential word problems

Practice: Interpret exponential word problems

**Background Notes** – percent of change vs amount of change

Example: 50% increase

Suppose our original amount is $100 and we’re going to increase this by 50%

Original amount: $100

New amount: $100 + 50% of $100

Notice: we keep 100% of our original + 50% of our original

So, really we get 150% of our original

New amount: 150% 0f 100 = 1.5 * 150 = $150

We can also see this using the distributive property

100 + 50% 0f 100

100 + .50 * 100

(1 + .50) * 100

1.5 * 100 (there is the 150% of 50)

Conclusion: a 50% increase is equivalent to finding 150% of the original.

Example: 50% increase every week

Time Amount

Week 0 $100

Week 1 150% of 100 = 1.5 * 100

Week 2 150% of 150% of 100 = 1.5 * 1.5 * 100 = 1.5^2 * 100

Week 3 150% of 150% of 150% of 100 = 1.5 * 1.5 * 1.5 * 100 = 1.5^3 * 100

Week 4 150% of 150% of 150% of 150% of 100 = 1.5 * 1.5 * 1.5 * 1.5 * 1.5 * 100 = 1.5^4 * 100

Here we make a generalization (write an expression for the amount for any given week)

Week x 1.5^x * 100 or 100 (1.5)^x

y = 100 (1.5)^x, where y is the amount of money in dollars

**7th Grade Students**

## Circumference and Area of Circles

Great job on section 6-2 (Surface Area of Prisms) from our textbook!!

*I will be entering participation grades into PowerSchool and emailing those students with missing assignments*

*Big Ideas Textbook/Khan Academy/i-Ready*

*Answers to problems 15, 17, 18, and 20 on pages 260-261*

#15: 449 in ^2.

The surface area of the box is 448 square inches, so that is the least amount paper needed to cover the box

#17: 156 in^2.

Note the top and bottom face is the trapezoid with base lengths of 12 and 6 and height of 4. To find the area of a trapezoid find half the sum of the 2 base lengths and then multiply by the height 4. The rest of the faces are rectangles.

#18: 68 m^2.

Only the front and back faces are parallelograms. The rest of the faces are rectangles.

#20: A company saves about $10.63 by using Box 2.

Note that even though each storage box has the same volume, their shapes are different.

Box 1: a long 20 inch-box with a width of 6 inches and a short height of 4 inches (volume of 480 cubic inches)

Box 2: a shorter 15 inch-box with a width of 4 inches, but a taller height of 8 inches (volume of 480 cubic inches)

Solution strategy:

Step 1: Find the surface area of each box in square inches

Box 1: 2(20 * 4) + 2 (20 * 6) + 2 (4 * 6) = 448 square inches

Box 2: 2 (15 * 8) + 2 (15 * 4) + 2 (8 * 4) = 424 square inches

We can see that Box 2 has less surface area and thus would require less material to make. But, now we need to find out how much we are going to save using Box 2. Note that the given unit cost of 1.25 is for dollars per square foot.

Step 2: convert square inches to square feet

reasoning: 1 square foot = 144 square inches; 4 square feet = 576 square inches.

So, to convert square feet to square inches, multiply by 144

And, to convert square inches to square feet, divide by 144

Box 1: 448 square inches is approximately 3.11 square feet

Box 2: 424 square inches is approximately 2.94 square feet

Step 3: Find the cost of each storage box

Box 1: 50 * (3.11 ft^2) * (1.25 $ / ft^2) = $194.38 (approximately)

Box 2: 50 * (2.94 ft^2) * (1.25 $ / ft^2) = $183.75 (approximately)

Step 4: Answer the question

A company saves about $10.63 using Box 2

**New Assignment – Khan Academy**

Ladies and gentlemen, I have assigned all of you the following videos and practice sets from Khan Academy to complete by Friday, high noon. And, yes, I can tell whether you are watching the videos and the problems you complete. I will provide feedback via your emails

Remember: Class code is DPJJQ6FM

Lesson Title: Area and Circumference of Circles (7th Grade, Geometry Unit)

Area and Circumference of Circles

Video: Radius, diameter, circumference and pie (11 minutes)

Video: Labeling parts of a circle (2 minutes)

Article: radius, diameter, and circumference

Practice Set: Radius and diameter (7 questions)

Video: radius and diameter from circumference ( 3 minutes)

Video: Relating circumference and area (4 minutes)

Practice Set: Circumference of a circle (4 questions)

Video: Area of a circle (4 minutes)

Practice Set: Area of a circle (7 questions)

If you need more time to complete, just let me know