Due in 6 hours... Original work and worksheet attached to be completed

1. Determine the population of your state 10 years from now.

According to the most recent census estimate, the population of Florida is 19,317,568 (World Population Review, 2013). Florida has a growth rate of 1.2%, and is ranked as the eighth fastest growing state in the country. (Clouser, 2012).

To determine the population 10 years from now, we use the following formula:

P(1 + r)n

P represents the initial population we are considering = 19,317,568

r represents the annual growth rate expressed as a decimal = 1.2/100 = 0.012

n is the number of years of growth = 10

Plugging these into the formula, we find:

19,317,568(1+0.012)10

=19,317,568(1.012)10

=19,317,568(1.127)

=21,770,899 = Population of Florida in 10 years.

2. Determine how long and in what year the population in your state may double assuming a steady annual growth rate.

We use the following formula:

Double P = P(1 + r)n 

P will be 19,317,568, Double P will be 38,635,136, r = 0.012, and we will be looking for n.

38,635,136 = 19,317,568(1+0.012)n Divide both sides by 19,317,568

2 = (1.012)n

To solve for n, we need to invoke a special exponent property of logarithms. If we take the log of both sides of this equation, we can move exponent as shown below:

log 2 = log (1.012)n log 2 = n log (1.012)

Now, divide both sides of the equation by log (1.012) to get:

n = log 2 / log (1.012)

Using the logarithm function of a calculator, this becomes:

n = log 2/log (1.012)

= 58.1 years to double the population of Florida

3. Look up the population and annual percentage growth rate of the city in which you live.

Tampa, Florida population: 347,645 Growth Rate: 1.8% (United States Census Bureau, 2012)

4.Determine the population of your city in 10 years .

P(1 + r)n

P is 347,645

r is .018

n is 10

347,645(1+0.018)10 Plug in the values

=347,645(1.018)10

=347,645(1.195)

=415,435= Population of Tampa in 10 years

5. Determine how long until the population of your city doubles assuming a steady growth rate.

We use the following formula:

Double P = P(1 + r)n 

P will be 347,645, Double P will be 695,290, r = 0.018, and we will be looking for n.

695,290 = 347,645(1+0.018)n Divide both sides by 347,645

2 = (1.018)n

To solve for n, we need to invoke a special exponent property of logarithms. If we take the log of both sides of this equation, we can move exponent as shown below:

log 2 = log (1.018)n log 2 = n log (1.018)

Now, divide both sides of the equation by log (1.018) to get:

n = log 2 / log (1.018)

Using the logarithm function of a calculator, this becomes:

n = log 2/log (1.018)

=38.9 years to double the population of Tampa

6. Discuss factors that could possibly influence the growth rate of your city and state.

Both the city of Tampa and the state of Florida are experiencing growth. The United Census Bureau ranked Tampa as the 3rd largest city in Florida (2010). Factors influencing the increases in population are migration from overseas and within the country. In fact, The World Population review (2012) suggests “around two thirds of residents were born in another state – a statistic that is the second highest in the US.” Florida also ranks fourth in illegal immigration, leading to a projection by The U.S. Census Bureau “that Florida will have gained 1.9 million additional immigrants between 1995 and 2025 (Bouvier and Stein, n.d.). Florida has no state tax, making it attractive to people from other states, and it is also a hotspot for retirees. As the baby boomers age, there is a great likelihood they will come to Florida to retire.

However, I must say that there is a grumbling about the population in Florida, as well as the city of Tampa. No state tax means a threatened infrastructure. Particularly, the traffic infrastructure, school systems, and environment all suffer because of rising population. Bouvier and Stein illustrate, “Its open space is vanishing, its highways are clogged with polluting traffic jams, and every day, 860 acres of its forests and farmland are lost to development” (n.d.). Perhaps these offenses will make people think twice before making the move to Florida. This could slow the growth rate and even reverse it if conditions get too bad.

If this were to happen, a 0.9% decline would look like this: Florida

P(1-r)^n

19,317,568 (1-0.009)^10

19,317,568 (0.991)^10

19,317,568 (0.9135) = 17,646,598 in ten years

Tampa P(1-r)^n

347,645 (1-0.009)^10

347,645 (0.991)^10

347,645 (0.9135) =317,573 in ten years

7. Think of other real world applications where exponential equations can be utilized.

“Exponential growth and decay are mathematical changes.  The rate of the change continues to either increase or decrease as time passes” (Roberts, 2012).

The formulas are:

Growth : y = a(1+r)x

Decay: y = a(1-r)x

Some examples include:

Money growing exponentially in a bank account

The price of products growing exponentially with inflation (Pirnot, 2010)

The decay of bacteria and radioactive substances (Jordan, 2013)

The decline (or decay) of participants in rounds of play during a tournament

-Heather

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