Name:Algebra 2
Date:
More Exponential Function Tables and Word Problems
Directions for 1 – 4: Write the equation for the table. (Hint: the table might not represent an exponential function)
1.
x / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7y / 6 / 9 / 12 / 15 / 18 / 21 / 24 / 27
y = ______
2.
x / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7y / 6 / 18 / 54 / 162 / 486 / 1458 / 4374 / 13122
y = ______
3.
x / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7y / 2 / 2.4 / 2.8 / 3.2 / 3.6 / 4.0 / 4.4 / 4.8
y = ______
4.
x / 0 / 1 / 2 / 3 / 4 / 5 / 6y / 2 / 2.4 / 2.88 / 3.456 / 4.1472 / 4.97664 / 5.971968
y = ______
Exponential Word Problems
Directions: The rest of these problems are word problems that represent EXPONENTIAL functions.
5.The bacteria E. coli often cause illness among people who eat infected food. Suppose that a singleE. coli bacterium in a batch of ground beef begins doubling every minute.
a.How many bacteria will there be after 1, 2, 3, 4, and 5 minutes have elapsed? (Assume no bacteria die.)
0 minutes:
1 minute:
2 minutes:
3 minutes:
4 minutes:
5 minutes
b.Write an equation that can be used to calculate the number of bacteria in the food after any number of minutes. Let x = # of minutes. y = # of bacteria.
y =
c.How many bacteria will there be after 20 minutes?
6.Suppose 50 E. coli bacteria are introduced into some food as it’s being processed, and the bacteria begins doubling every 10 minutes.
a.Complete this table showing the number of bacteria from stage 0 to stage 6 of the process.
Stage of the process / 0 / 1 / 2 / 3 / 4 / 5 / 6Number of good deeds / 50 / 100
b.Write a function formula relating the variables x = the stage of the calling process and
y = the number of bacteria present at that stage.
c.After 120 minutes have passed, how many bacteria are present?
(Hint: First you’ll have to think about how many stages have passed in 120 minutes.)
7.My nephew likes to rip up pieces of paper. Suppose he got his hands on a pile of 20 quiz papers. They rip all the quizzes in half, so now they have 40 pieces of paper. Then they rip all the pieces in half again, and so on.
Let x = # of times he rips up the pages. Let y = # of pieces of paper
a. Fill in the table.
# of times my nephew rips up the papers / 0 / 1 / 2 / 3 / 4 / 5 / 6# of pieces of papers / 20 / 40
b. What is the starting number of pieces of paper?
c. What number do you multiply by as you go across the table?
d. Write an equation for the number of pieces of paper (y).
y =
8.Suppose that as a New Year’s Resolution you decided to save your money in the following way. Before the start of the year, you had $0.25 in a piggy bank. Each day you would double the money in your piggy bank. So on January 1, you would have $0.50 saved. On January 2, you would have $1.00 saved, and so on.
Let y stand for the amount you would have saved as of day x of January.
a.Without a calculator, fill in the output column of the table
Date / x / y /Dec. 31 / 0 / 0.25
Jan 1 / 1 / 0.50
Jan 2 / 2 / 1
Jan 3 / 3
Jan 4 / 4
Jan 5 / 5
Jan 6 / 6
Jan 7 / 7
b.Write a function formula for y.
y = ______
c.Graph the points on the grid.
d.Sketch the graph of y by drawing a curve that goes through the points.
e.If you kept up this process, how much money would you have on January 31?