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.