8th GRADE STUDENTS, MARCH 18, Wednesday
Quick announcement: I notice some of you were unable to view the assignments. Please don’t worry. We’re just getting started.
It is helpful to watch the videos below from Khan, Algebra I, Exponential Growth and Decay, Exponential vs Linear Growth, as I saw that most of you did.
View video 1: Intro to exponential functions (7 min, 40 sec)
View video 2: Exponential vs Linear Growth (3 min, 5 sec)
View video 3: Exponential vs linear models: verbals (3 min, 28 sec)
View video 4: Exponential vs linear models: tables (3 min, 26 sec)
We are now going to switch back to our beloved textbook
Lesson Tool: Big Ideas Textbook (access online)
Lesson Title: Exponential Functions (6.4), page 286
Goal: I can write and graph exponential functions by examining the growth pattern and determining whether the data represents a linear or an exponential function
A single bacterium, splitting in two every 20 minutes, would produce nearly 5000 billion-billion bacteria in day.
There are 72 of these 20-minute time periods in a 24-hour day
500 billion-billion? This is 5000 x 10^9 x 10^ 9 = 5 x 10^21 , or in standard form, a 5 followed by 21 zeros
The type of function you will be examining today can be used to model bacteria population growth
Lesson Notes (top of page 286):
A function of the form y = a (b)^x (a cannot equal 0, b cannot equal 1, and b > 0) is an exponential function
The exponential function y = ab^x is a nonlinear function that changes by equal factors over equal intervals
Note: the independent variable x is attached to the base b and not to the coefficient a
Skill #1 – Identifying Functions
the difference between each successive y-value is the same: 4 – 2 = 6 – 4 = 8 – 6 = 2
y = 2x + 2 can model this table (y = mx + b)
2 is the initial value, and 2 is the constant rate of change
the ratio between each successive y-value is the same: 8/4 = 16/8 = 32/16 = 2
y = 4 (2)^x can model this table (y = a (b)^x)
4 is the initial value and the function increases by a factor of 2 (it doubles) for each 1-unit increase in x
Skill #2 – Evaluating Exponential Functions
order of operations tells us to evaluate the power before multiplying
evaluate y = -2(5)^x when x = 3
evaluate y = 3(0.5)^x when x = -2
Assignment (please email your answer to email@example.com)
Textbook, Page 289, #s 6 – 15 ALL
DUE: Let’s say by 11:00 A.M. THURSDAY
7th GRADE STUDENTS, MARCH 18, Wednesday
Learning Tool: Big Ideas Math Accelerated textbook (can be accessed online)
Lesson 6.2: Surface Area of Prisms (Chapter 6 – Surface Area of Solids)
Goal: I can find the surface area of a prism by finding the sum of the area of the bases and lateral faces
Solutions to yesterday’s HW (#’s 6 – 14, page 260):
6. 94 in^2 7. 72 cm^2 8. 162 cm^2 9. 130 ft^2 10. 198 cm^2 11. 76 yd^2 12. 17.6 ft^2 13. 136 m^2 14. 57.1 mm^2
Assignment due tomorrow, Thursday, March 19
Students are to complete problems 15, 17, 18, 20 and submit their answers to my email address by March 18, Wednesday morning, 11:00 A.M.
Problem #20 Hint
This is a classic type of problem in manufacturing. For a given volume, what is the least amount of material I can use? The general answer is that the more cube-like, the more efficient use of material. For instance, a cube-like tissue box is much more cost effective than a cereal box.
Each storage box has a volume of 480 cubic inches. However, the shapes are quite different.
Step 1: find the surface area of each box in square inches
Step 2: We need to convert the above values into square feet (note that 1 square foot = 144 square inches)
Step 3: Find the cost of each type (making 50 boxes and the cost is 1.25 $/ft^2)
Step 4: Find the difference in prices