Growing 3 1 & 3 2
View more documents from Kathy Favazza.
Wednesday, March 31, 2010
Tuesday, March 30, 2010
Math Reflection
1) You can recognize an exponential decay pattern from a table of data if it is divided my the same number each time.
2) You can recognize an exponential decay pattern from a graph when the line slopes down.
3) You can tell that an equation represents exponential decay if the growth factor is less than 1.
4) Exponential growth relationships and exponential decay relationships are similar because they both use exponents, they have growth/decay rates, and they both have growth/decay factors. They are different because exponential growth relationships have a growth factor greater than 1, when an exponential decay's is less than 1.
5) Exponential decay relationships and decreasing linear relationships are similar because they both decrease. They are different because exponential decay relationships are divided by the same number each time, while decreasing linear relationships get the same number smaller each time.
2) You can recognize an exponential decay pattern from a graph when the line slopes down.
3) You can tell that an equation represents exponential decay if the growth factor is less than 1.
4) Exponential growth relationships and exponential decay relationships are similar because they both use exponents, they have growth/decay rates, and they both have growth/decay factors. They are different because exponential growth relationships have a growth factor greater than 1, when an exponential decay's is less than 1.
5) Exponential decay relationships and decreasing linear relationships are similar because they both decrease. They are different because exponential decay relationships are divided by the same number each time, while decreasing linear relationships get the same number smaller each time.
Monday, March 29, 2010
Math Reflection 3
1.
a. If you know the initial value for a population, and you know the yearly growth rate, you can make an equation. For example, starting population=500, yearly growth rate=80%. To change the growth rate to the growth factor, you change the percent to a decimal, and add 1. The equation for this situation would be 500(1.8^x). If you want to find out the population after, say, 5 years, just plug in 5 for x, 500(1.8^5). The answer is 9447.84.
b. The growth rate of an equation is the growth factor of an equation, times 100 (as a percent). If the growth factor was 1.6, the growth rate would be 160%.
2.
a. If you know the initial value of a population and the yearly growth rate, you can make an equation. If the beginning population was 200, and yearly growth factor was 1.3, the equation would be 200(1.3^x). If you wanted to know the population 7 years from now, you would just plug in 7 for the x. The answer is 200(1.3^7), or 1254.97034.
b. You can determine the yearly growth rate by multiplying the growth factor by 100.
3. To get the population when it doubles, just multiply the starting value by 2. Then, guess and check what the x value is(the year), when the population doubles. When it is about the starting value times 2, that is it.
a. If you know the initial value for a population, and you know the yearly growth rate, you can make an equation. For example, starting population=500, yearly growth rate=80%. To change the growth rate to the growth factor, you change the percent to a decimal, and add 1. The equation for this situation would be 500(1.8^x). If you want to find out the population after, say, 5 years, just plug in 5 for x, 500(1.8^5). The answer is 9447.84.
b. The growth rate of an equation is the growth factor of an equation, times 100 (as a percent). If the growth factor was 1.6, the growth rate would be 160%.
2.
a. If you know the initial value of a population and the yearly growth rate, you can make an equation. If the beginning population was 200, and yearly growth factor was 1.3, the equation would be 200(1.3^x). If you wanted to know the population 7 years from now, you would just plug in 7 for the x. The answer is 200(1.3^7), or 1254.97034.
b. You can determine the yearly growth rate by multiplying the growth factor by 100.
3. To get the population when it doubles, just multiply the starting value by 2. Then, guess and check what the x value is(the year), when the population doubles. When it is about the starting value times 2, that is it.
Math Reflection 3
1. A) If you know the initial value and the growth rate of the population you can make an equation using the format y=a(b)^n. Say the initial value was 1000 and the growth rate was 4%, you first need to make the growth factor. You do this by making the percent into a decimal, (.04), then you add 1, (1.04), your equation would be y=1000(1.04)^n. to figure out the population in a certain amount of years you just put the number in as x and solve.
1. B) The growth rate is related to the growth factor because the growth factor is the rate in decimal form plus 1.
2. A) You do the same as above. You take the initial value and growth factor and put them into an equation. Then you put the number of years s x then solve.
2. B) You can determine the growth rate by first subtracting 1. Then you multiply the decimal by 100 to get the percent.
3. To find the doubling point of the population you take the initial value and double it. So now the equation is y=2p(b)^n. From there you take an educated guess to see it when you plug x in (number of years) it doubles. If it doesn't you go up or down from there to see when the doubling point is.
Math Reflection
1. a) To determine the population many years from now you have to figure out the growth factor. To do this, you change the percent to a decimal and add one. For example, if the growth rate is 20%, the growth factor is 1.2. You would then take the growth factor and the initial value and put it into this equation: y=a(b)^x.
y=total, a=initial value, b=growth factor, x=number of years.
If the initial value is 200 and the growth factor was 1.2 the equation would be y=200(1.2)^x.
b) The growth rate is related to the growth factor because they are the same thing just written differently. To change the growth rate (which is a percent) to the growth factor (a number...usually a decimal) you divide by 100 and add 1. To change the growth factor to the growth rate you subtract 1 and multiply by 100. (It's doing the opposite of changing the growth rate to the growth factor).
2. a) If you know the initial value and the growth factor you can just plug it into this equation to find out the total for any number of years. The equation is: y=a(b)^x.
y=total, a=initial value, b=growth factor, x=number of years.
b) To determine the yearly growth rate you subtract 1 from the growth factor and multiply by 100.
3. If you know the equation that represents the exponential relationship between the population and the number of years you can determine the doubling time for the population by first figuring out 2p. After that you plug that value into the equation p=a(b)^x to solve for x. The x will give you how long it will take for the population to double.
Math Reflection from Page 47
#1 When you know the initial value and yearly growth rate, it is simple to determine a population from year to tear. First, convert the growth rate to a growth factor by putting the growth factor into decimal form and adding 1. For example if the growth rate is 7% then 7% in decimal form is 0.07 and 0.07+1=1.07. The growth factor is 1.07. Next, start the equation with the initial population. Then multiply that with the growth rate to the power of the year. For example, if the initial population is 1,000 and the growth factor is 1.07, then the population in 4 years corresponds to the equation 1000(1.07)^4. The population is about 1310 in 4 years. Growth factor and growth rate are closely related. Growth rate is really growth factor but in percent form without including the current sum. Growth factor is growth rate plus one and in the decimal form.
#2 If you know both the initial value and the growth factor, finding a population in a few years is even simpler. All you need to do is multiply the initial value times the growth rate to the power of the year. If the initial population is 10,000 and the growth rate is 1.1 the population is 6 years is found with the following equation: 10,000(1.1)^6.
#3 To determine the doubling population's sum, you use the following equation p= 2^n. This means population equals the growth factor (2) to the power of the year, n.
Kate :-)
#2 If you know both the initial value and the growth factor, finding a population in a few years is even simpler. All you need to do is multiply the initial value times the growth rate to the power of the year. If the initial population is 10,000 and the growth rate is 1.1 the population is 6 years is found with the following equation: 10,000(1.1)^6.
#3 To determine the doubling population's sum, you use the following equation p= 2^n. This means population equals the growth factor (2) to the power of the year, n.
Kate :-)
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