Exponential Functions Day 2

Exponential GrowthInflation means that a current dollar will buy less in the future.

According to the US Consumer Price Index, the inflation rate for 2005 was 4%. This means that a one-pound loaf of white bread that cost a dollar in January 2005 cost $1.04 in January 2006.The change in price is usually expressed as an annual percentage rate, known as the inflation rate.

1. At the current inflation rate of 4% how much will a $20 pair of shoes cost next year?

2. Assume that the rate of inflation remains at 4% next year. How much will the shoes cost in the year following next year.

Fill in the Table and GraphYears From

Now,xCost of the

shoes, y

or f(x)

0 20

1 20.80

2 21.63

3

4

10

Find the Equation

Exponential Decay

You have just purchased an automobile for $16,000. Much to your dismay, you have just learned that you should expect the value of your car to depreciate by 15% per year. First find the equation.

Determine the value of the car in 6 years.

During a meeting, you hear the familiar ring of a cell phone. Without hesitation, several of your friends reach into their jacket pockets, brief cases, and purses to receive the anticipated call. Although sometimes annoying, cell phones have become part of our way of life.The following table shows the rapid increase in the number of cellular phones (figures are approximate) in the late 1990s. Note that the independent variable (year) increases in steps of one unit (year).

How long will it take for any given number of cell phone users to double?

You have just purchased a new car for $26,000. Much to your dismay, you just learned that you should expect the value of your car to depreciate by 30% per year! The following table shows the book value of the car for the next several years where V is the value in thousands of dollars

How long will it take for any specific value of the car to halve?

Assignment

• Yarn Activity