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.