1.a. You can use a table to find the y-intercept of an exponential relationship by finding the dependent variable's value when the independent variable's value is 0. When finding the y-intercept of an exponential relationship in a graph, you look to see where the line crosses the y-axis. To find the y-intercept of an exponential equation, you substitute 0 for the independent variable and solve for y. You could also find this by looking for a in the equation y=a(b^X).
You find the growth factor of an exponential relationship from a table by calculating what the dependent variable is multiplied by every time the independent variable increases by 1. To find the growth factor from a graph, find what the dependent variable is multiplied by every time the independent variable increases by 1. This is just like a table, only you use points on the line. The growth factor in the equation is b in the equation y=a(b^X).
1.b. The y-intercept is a in the equation y=a(b^X). The growth factor is b in this equation. To create an exponential relationship's equation, you simply substitute these numbers in for a and b in the equation.
2.a. In the equation y=a(b^X), a is the initial value of the exponential relationship, and b is the growth factor of the exponential relationship.
2.b. In a graph of y=a(b^X), a is the y-intercept.
2.c. In a graph of y=a(b^X), b is the amount y is increased by every x, or the steepness of the line.
Monday, March 22, 2010
Mathematical Reflection 2
1. a. You can use a table to find the y-intercept and growth factor from an exponential relationship. To find the y-intercept you look or extend the table to when x is 0. You can find the growth factor by finding the relationship between the y section in the table.
b. You use the y-intercept and growth factor to form an equation. You use the form, y=a(b^x). A is the y-intercept and b is the growth factor. You plug the numbers in and form an equation.
2. a. In an exponential relationship you use the equation y=a(b^x). The A is the y-intercept (initial value). B is the growth factor.
b. A is represented because it is the y-intercept .
c. B is represented because it is the growth factor, so it affects the steepness of the curve. It is sort-of like the slope of a line.
b. You use the y-intercept and growth factor to form an equation. You use the form, y=a(b^x). A is the y-intercept and b is the growth factor. You plug the numbers in and form an equation.
2. a. In an exponential relationship you use the equation y=a(b^x). The A is the y-intercept (initial value). B is the growth factor.
b. A is represented because it is the y-intercept .
c. B is represented because it is the growth factor, so it affects the steepness of the curve. It is sort-of like the slope of a line.
Monday 3/22/10: Fractional Growth Factors
Today in class, we went over the Exploring Exponential Functions worksheet we started on Friday. We determined the effect of a, b, and c of the graph of the equation y=a(b^x)+c:
We were introduced to fractional growth factors today. We saw that whether the growth factor was fractional or not did not effect the form of the equation. We did a problem in class about rabbits. We were given a table of the growth of a particular rabbit population. Using the information, we found that the growth rate was about 1.8. This did not influence the appication of y=a(b^x) to its graph.
- a is the starting point of the equation. It is the original y-intercept. When a is a negative number,the line of the equation points downward. On the other hand, when a is a positive number, the resulting line points up, giving it a shape similar to an U.
- b is the growth rate of the equation. It defines the steepness of the graph.
- c shifts the curved line up or down on the y-axis. When added to the a value of the equation, it results in the final y-intercept of the graph.
We were introduced to fractional growth factors today. We saw that whether the growth factor was fractional or not did not effect the form of the equation. We did a problem in class about rabbits. We were given a table of the growth of a particular rabbit population. Using the information, we found that the growth rate was about 1.8. This did not influence the appication of y=a(b^x) to its graph.
Mathematical Reflections 2
1.
a. The growth factor in an exponential line is how steep the curve is. The y-intercept is where the line starts on the y-axis. In a table, you divide the y of any x by the y of the x before it, and you get the growth factor. In a graph, you do the same, only you have to find the points, and divide the y values. In the equation y= a(b^x), b is the growth factor. To find the y-intercept in a table, you just look to where the x=o. On a graph, you just look at where the line crosses the y-axis. In the equation y=a(b^x), the y-intercept is a.
b. If you know what the y-intercept and growth factor are, you can plug them into the standard equation y= a(b^x).
2.
a. The a is the y-intercept, the b is the growth factor.
b. a is the y when x=o, and where the line crosses the y-axis
c. b is the steepness of the line.
a. The growth factor in an exponential line is how steep the curve is. The y-intercept is where the line starts on the y-axis. In a table, you divide the y of any x by the y of the x before it, and you get the growth factor. In a graph, you do the same, only you have to find the points, and divide the y values. In the equation y= a(b^x), b is the growth factor. To find the y-intercept in a table, you just look to where the x=o. On a graph, you just look at where the line crosses the y-axis. In the equation y=a(b^x), the y-intercept is a.
b. If you know what the y-intercept and growth factor are, you can plug them into the standard equation y= a(b^x).
2.
a. The a is the y-intercept, the b is the growth factor.
b. a is the y when x=o, and where the line crosses the y-axis
c. b is the steepness of the line.
Yesterday, our class worked on graphing Exponential Functions in order to learn how certain variables effect the function's graph. In the equation y=a(b)*+c the variables a, b and c all change the way the graph looks. The a is the y-intercept or initial value, unless there is a c in the equation. If there is a c, the two variables values are added to create the y-intercept. The b in the equation is the growth factor. It represents the rate that the line is increasing or decreasing much like the slope does in a linear equation. For example, if the b is two, then the y is doubling every interval. Next, the c is, again, the added or subtracted variable that is able to change the y-intercept and the a. The c sometimes is the y-intercept when you add one to it, because in many Exponential Functions the initial factor (a) is one. These three important variable can reveal a lot of information about an Exponential Function's graph.
Mathematical reflections 2
1. a. You can find the y-intercept in an exponential relationship by using a table, a graph, and an equation. You can find the y-intercept from a table by looking at the y when the x is zero on the table. Whatever the y is will be the y-intercept. you can find the y-intercept from a graph by looking at where the line passes the y axis and that will be the y-intercept. You can find the y-intrcept from an equation by looking at the number that is being multiplied by a number with an exponent and that will be the y-intercept.
You can also find the growth factor in an exponential relationship by using a table, a graph, and an equation. you can find the growth factor from a table by looking at ho much y is being multiplied by for each x and that will be the growth factor. You can find the growth factor from a graph by looking at how much y is multiplied on the graph for every x and that will be the growth factor. You can find the growth factor of an equation by seeing what number has an exponent and that will be the growth factor.
1. b. You can use the y-intercept and growth factor to write an equation for an exponential relationship. You can put the y-intercept first and have it multiplied by the growth factor with an exponent of whatever number x the problem is at.
2. a. In the equation y=a(b^x), a is the initial value of the exponetial relationship and b is the growth factor of the exponetial relationship.
2. b. In a graph of y=a(b^x), a is the y-intercept.
2. c. In a graph of y=a(b^x), b is the amount y goes up for every time x goes up one interval or the steepness of the line.
You can also find the growth factor in an exponential relationship by using a table, a graph, and an equation. you can find the growth factor from a table by looking at ho much y is being multiplied by for each x and that will be the growth factor. You can find the growth factor from a graph by looking at how much y is multiplied on the graph for every x and that will be the growth factor. You can find the growth factor of an equation by seeing what number has an exponent and that will be the growth factor.
1. b. You can use the y-intercept and growth factor to write an equation for an exponential relationship. You can put the y-intercept first and have it multiplied by the growth factor with an exponent of whatever number x the problem is at.
2. a. In the equation y=a(b^x), a is the initial value of the exponetial relationship and b is the growth factor of the exponetial relationship.
2. b. In a graph of y=a(b^x), a is the y-intercept.
2. c. In a graph of y=a(b^x), b is the amount y goes up for every time x goes up one interval or the steepness of the line.
Math Reflection 2
1a. The growth factor of an expenentionally grown line is the steepness. It shows how fast it goes up for example doubling or tripleing. To find it in in a table you divide y when x equals 2 by y when x equals 1. To get it from a graph you do the same thing from the table exept you have to find the points. From the equation: Y= a(b to the x) the growth factor is the b. To find the y intercept in a table or graph you take the number when x is zero. To find it from the equation you fill in 0for x or take the a value.
1b. You fill in the Y intercept as the a value and the growth factor for the b value.
2a. A is the y intercept b is the growth factor.
2b. A is the spot where x equals 0.
2c. B is how rapidly the line is going up.
1b. You fill in the Y intercept as the a value and the growth factor for the b value.
2a. A is the y intercept b is the growth factor.
2b. A is the spot where x equals 0.
2c. B is how rapidly the line is going up.
Subscribe to:
Posts (Atom)
