Growing, Growing, Growing Problem 2.1

Growing, Growing ,Growing Problem 2 1

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Exponential Growth

Today in class we finished up the problem we started yesturday, The Kingdom of Monterak. We also started problem 2.1 in the Growing, Growing, Growing book. Both these problems have to do with exponential growth. Exponential growth is based on the growth factor.

The growth factor-
-the fixed number of increase (ex. doubling, tripling)
-the base in the equation (see below)
-the ratio of change from one y value to the next.

When you do these kind of problems, you should use an equation like this.

y=a(b)[to the x power]

The y is the dependant variable.
The x is the independent variable. (the exponent)
The a is the initial value. (the y-intercept)
The b is the growth factor.

:) :)

March 15

Today in class we started a problem called The Kingdom Of Marteka. It had to do with equations including exponents. There were five different plans for a reward for a peasent. All of the plans had a different number of squares on the board number of rubas per first square and the rate they went up. For each plan they had a different equation and we had to find it. An example of one of the equations was 2 to x-1 power.


Standard notation is just a number or answer to a problem in number form. Scientific notation is another way of writing the answer to a problem with exponents. Its written in the form a times ten to the power of b. If the answer is too big they use scientific notation to simplify by earasing zeros.


During the proble we have to figure out how many rubas will be on the last tile and how many will be on the whole board. The king kept trying to change the proposal but, was really bad in math.

Problems 5.3 and 5.4

Today in class we did problems 5.3 and 5.4.

In problem 5.3, there were various problems about graphing inequalities. We learned that when y is greater than or equal to mx+b, the shaded region is above the line of the inequality, and when y is less than or equal to mx+b, the shaded region is below the line. We also learned that when the sign in the inequality is greater than/less than or equal to, the line is solid and when y cannot be equal to mx+b, the line is dashed.

In problem 5.4 we learned how to graph two inequalities, or a system of linear inequalities, on the same axis. The region where both shaded areas overlap contains all the points that satisfy both inequalities.

Solving Systems of Linear Equations with matrices

Elimination Method

In class on Thursday, we reviewed the three ways to solve systems we knew; graphing, setting equal, and substitution. Then we learned the 4th method, Elimination.

For example,

4x+5y=47
8x+2y=38
You would multiply the first equation by 2
2(4x+5y=47)
8x+10y=94
Then you would subtract the second equation from the first, cancelling out the x
8x+10y=94
- 8x+2y=38
8y=56
y=7

Then you would substitute in 4 for x
4x+5(7)=47
4x+35=47
4x=12
x=3
The answer to the system is (3,7).
TIPS
You can solve for either the x or the y.
Sometimes you may have to multiply both equations to be able to cancel out a variable.
You can add or subtract the equations to get an answer.

Systems of Linear Equations word problems

Ch. 7 4 Intro

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