Hard to believe that we had this snow storm in October!
School had to be cancelled because Newton City deciding to close all buildings. We will wait to see how the school schedule is adjusted. Stay tuned.
I had prepared candies for students. I guess now I will eat them, all by myself! 🙂
Today’s topics are exponential growth functions and exponential decay functions.
An exponential growth function can be written as the following:
y = C(1+r)^t
where t represents time, r is called growth rate (r > 0), 1+r is called growth factor, C is in the initial value.
A good example to help understand the exponential growth function is the simple bank annual interest. r will be the annual interest rate, t represents number of year, C is the initial deposit, and y is the total amount after t years.
Similarly, an exponential decay function can be written as the following:
y = C(1-r)^t
where t represents time, r is called decay rate (1 > r > 0), 1-r is called decay factor, C is the initial value.
A good example would be car losing value as 10% per year.
This lesson finishes the chapter 8. Next time we will do a review of what we have learned in the first 6 lessons, to get ready for the mid term exam two weeks from now, on 11/6.
Here is the homework:
http://blog.newtonchineseschool.org/wangweidong/files/2011/10/Math7_Fall_HW_L6.pdf
Dear Parent/Student:
Today we first went over the exponential functions again as some students found that part of the homework difficult. We then continued our Exponents study with section 8.3 and 8.4. We further talked abut the division properties of exponents:
a^m / a^n = a ^ (m-n), a <> 0 and
(a / b)^m = a^m / b^m, b <> 0
We did some exercises on simplifying expressions with exponents. I think students are still not good at dealing with negative exponents and how to make a negative exponents positive with: (a /b) ^ (-m) = (b / a)^m. This takes practice to get better.
We then talked about scientific notation where a positive number can be represented as C*10^n, where 1<= C < 10, and n is an integer. We talked about how to convert from a decimal number to a scientific notation number and vice versa, how to do multiplication and division with scientific numbers.
Below is this week’s homework:
http://blog.newtonchineseschool.org/wangweidong/files/2011/10/Math7_Fall_HW_L5.pdf
²Today we started Chapter 8 about Exponents and Exponential Functions.
We covered the first two sections: Multiplocation Properties of Exponents, and Zero and Negative Exponents.
Basic take-aways are:
I didn’t get chance to cover the real world use cases. One example is like, there are two circular fields, one’s radium is twice the other, what is the area ratio. To solve it, you assume the smaller one’s radium as r, so the ratio is π(2r)²/πr² = 4.
I also had less time to go over the exponential functions, so if the student feels uncomfortable about the homework questions on exponential functions, they can skip. But if the parent can help explain, that will be great. I will circle back next time.
Homework is below:
http://blog.newtonchineseschool.org/wangweidong/files/2011/10/Math7_Fall_HW_L4.pdf
