Practice with Applied Exponential
Growth and Decay
Topic Index | Algebra Index | Regents Exam Prep Center

 

For each of the situations described below,
develop a chart, an equation and a graph to illustrate the data.
Grab your graphing calculator.

 

1.

The Fable of the Chess Board
and the Grains of Wheat

 

There is a well-known fable about a man from India who invented the game of chess, as a gift for his king.  The king was so pleased with the game that he offered to grant the man any request within reason.  The man asked for one grain of wheat to be placed on the first square of the chess board, two grains to be placed on the second square, four on the third, eight on the fourth, etc., doubling the number of grains of wheat each time, until all 64 squares on the board had been used.  The king, thinking this to be a small request,  agreed.  

A chess board has 64 squares.
How many grains of wheat did the king have to place
on the 64th square of the chess board?

Your Tasks:
a.  Complete the chart:

Number of the doubling 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 63
Wheat on each square 2                              
Pattern: 21                              

b.  Write a function to illustrate the situation.

c.  Plot the data and graph the function for squares 1 through 10.
 

 

 

 

2.

Rabbit Population Growth

 

In 1995, there were 85 rabbits in Central Park.  The population increased by 12% each year.  How many rabbits were in Central Park in 2005?

Your Tasks:
a.  Complete the chart:

Years 1
1996
2
1997
3
1998
4
1999
5
2000
6
2001
7
2002
8
2003
9
2004
10
2005
Number of Rabbits
(Round to the nearest rabbit.)
95                  

b.  Write a function to illustrate the situation.

c.  Plot the data and graph the equation.
 

 

 

3.

Bacteria Growth

 

A scientist has discovered a new strain of bacteria.  The bacteria culture initially contained 1000 bacteria and the bacteria are doubling every half hour.

Your Tasks:
a.  Complete the chart for the first five hours:

Time intervals
30 minutes
1
.5 hr
2
1 hr
3
1.5 hr
4
2 hr
5
2.5 hr
6
3 hr
7
3.5 hr
8
4 hr
9
4.5 hr
10
5 hr
Bacteria present 2000                  
Pattern:                    

b.  Write a function to illustrate the situation.

c.  Plot the data and graph the function for the first 4 time intervals.

d.  From your graph, determine how many bacteria are present after 45 minutes.

 

 

4.

Radium Decay

 
In 2000, 50 grams of radium were stored.  The half-life of radium is 1,620 years.  How many grams of radium remains after 4860 years?  Remember, half-life is the amount of time it takes for half of the amount of a substance to decay.

Your Tasks:
a.  Complete the chart:

End of Half life cycle  1
1620 yrs
 2
3240 yrs
3
4860 yrs
Grams of radium remaining      
Pattern:      

b.  Write a function to illustrate the situation. 

c.  Plot the data and graph the function.