Math Reflection 3

1a. To determine the population several years from the start using the initial value and the yearly growth rate, you can form an equation. To do this, you use the form of y=a(b^x) (a=initial value, b=growth factor, y=dependent variable, x=independent variable). Also, it's important that you take the growth rate, and convert it into its growth factor by taking the percent and adding 1 to its decimal form.
1b. A growth rate is the percent form of a growth factor. For instance, if a growth rate were 75%, its growth factor would be 1.75 because you have to take in account 100% of the previous value, plus the 75% that is going to be added to form the next value of y.

2a. To determine the population several years from the start using initial value and the yearly growth factor, you will also need to form an equation, only this time, there is no need to turn the growth rate into a growth factor, because there is no growth rate at all. Yet again, you use the form of y=a(b^x).
2b. You can determine the yearly growth rate by subtracting 1 from the number that is the growth factor and turning it into a percent.

3. If you know the equation that represents the exponential relationship between the population size p and the number of years n, you can determine the doubling time for the population by finding what 2p is, then finding the value of n that is closest to that amount.