Mathematical Reflections 3

1.a. If the initial value and growth rate of a population are known, you can easily determine the population several years from now. First, you must change the growth rate into the growth factor. The growth factor is usually in decimal form, but most important is that for exponential growth it is at least 1 or greater. Then, you just multiply the initial value by the growth factor raised to the n power.

b. The growth rate represents by how much the initial value increases each year, and the growth factor is what it is multiplied by each year. For example, the growth factor would be 1.7 when the growth rate is 70%. (The growth factor must have a 1 during exponential growth in order to make sure that the initial value is kept along with the increase.)

2.a. To find the population from the initial value and growth factor, you would again use the y=a(b)^x form, except this time you don't need to convert anything.
b. To determine the yearly growth rate, you subtract 1 from the growth factor if it is less than 2.

3. To find out how long it will take for a population to double, all you have to do is make y twice the initial value. Another thing you could do is to keep multiplying by the growth factor until the outcome is double or more the initial value.