Exponential Functions

1. A limited amount of light reaches a point under water. For a particular body of water, the amount of light reaching a specified depth is:

y = 0.6^x

where x is the depth in feet and y is the fraction of light reaching that depth (1.00 = 100% and 0.00 = 0%).

Graph this function.
How much light reaches a depth of 10 feet?
At what depth is the amount of light 50% what it is at the surface?

2. Your head gets larger as you grow. Yet most of the growth comes in the first few years of life. There is very little additional growth after you reach adolescence. The percent of adult size for your head is:

y = 100 - 80 ( 0.75^x)

where x is your age in years and y is the percent of adult size.

Graph this function.
What percent of adult size is a 2 year old child's head?
What percent of adult size is your head?

3. The following table presents the population of the United States from 1790 until 1960.

Year	Population
1790	3900000
1800	5300000
1820	9600000
1840	17100000
1860	31400000
1880	50200000
1900	76200000
1920	106000000
1940	132000000
1960	179000000

Find an exponential function y = ab^x that best describes this data.
Use this function to predict the population of the U.S. this year.
Find the estimated population of the U.S. this year.
Graph this data