Math Reflection

MATH REFLECTION

1a. Provided you were knew the initial population and growth rate, finding the population x years is really quite simple. All you need to do is turn the growth rate into a growth factor. You do this by turning the percentage given to you as a growth rate and change it to a decimal or integer. You will then add one to the number you get from the growth rate. This number is a vital part of this process, as it will be the base of the exponent in the equation. You would then right an equation for maximum clarity.

EXAMPLE:

Initial Population: 100

Growth Rate: 5%

Growth Factor: 1.05

Equation: Y=100(1.05 to the power of x)

You now choose the number of years and sub that in for x. After solving you should know the population.

1b. Growth rate and growth factor are very closely related. The growth rate is a percent and the factor a number. The growth rate shows the rate at which each number changes in the equation. While the growth factor is the number that "physically" represents the rate in the equation and is the base of the exponent in the equation.

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2a. If you had the initial population and the growth factor of a situation finding the population after a set number of years would be simple. All you would need would be to right an equation. This is easy because you are provided with all the needed elements of the equation. You would make the population (a variable) equal the initial value multiplied by the growth rate to the power of a variable representing the number of years that have passed.

EXAMPLE

Initial Value: 24

Growth Factor: 1.24

Equation: Y = 24(1.24 to the power of x)

2b. When given the growth factor finding the growth rate is not hard. You turn the growth factor into a percentage and then subtract 100%. You can also subtract one from the factor and then turn in into a percent.

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3. In order to determine the doubling point of a population when given the equation of that situation you would need to find the exponent that will bring the growth factor to two. This will then double the initial population. Finding the exponent that doubles the factor is purely educated guess and check.

Nick S.