Mathematical Reflections 3

1)
a. You can determine the population in several years from now by making a equation out of what you know. The formula is y=a(b^x). Since you know the initial value, plug it in to the "a". Then change the growth rate to a growth factor. You can do this by dividing one hundred and adding 1. Then, plug it into "b". Then, you can plug in the amount of years that you want to solve for in the "x", and solve the equation.

b. The growth rate is the percentage of growth between each year in this case. To find the growth rate from a growth factor is to subtract the 1 and multiply by 100. To find the growth factor from a growth rate is to add the 1 and divide by 100. The reason that the growth rate doesn't have the 1, and the growth factor does is because the growth factor is already the original value and the growth. The growth rate is only the growth and not the original value.

2)
a. As I said before, you could use the equation, y=a(b^x). Plug the initial value into "a". Then, as a step less from question 1a, you can just plug in the growth factor. Then, plug in the amount of years that you want to solve for in the "x" then solve.

b. You can determine the yearly growth rate by the growth factor. Subtract the 1 from the growth factor and multiply by 100.

3) You could do two things to determine the doubling time for the population. You could plug in twice the amount of the initial value in to "y", to make it equal that number. Then, you could solve for "x". Or you can do the guess and check method that I usually use. Plug in twice the initial value for "y", but guess a number for "x" and work your way around that to determine the correct answer.