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 :-)