Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
1) Suppose that a photocopy machine can reduce copies to 65 percent of their original size. By copying an already reduced copy, further reductions can be made.
a) If a page is reduced to 65 percent, what percent enlargement is needed to return it to its original size?
answer = ( ) percent
b) Estimate the number of times in succession that a page must be copied to make the final copy less than 15 percent of the size of the original.
number of times = ( )
3) The fox polulation in a certain region has an annual growth rate of 6 percent per year. It is estimated that the population at the beginning of the year 2000 was 19400.
(a) Find a function that models the population t years after the start of 2000.
P(t)= ( )
(b) Use the function from part (a) to estimate the fox population at the beginning of the year 2015.
P= (the answer should be an integer)
4) A glacier covered about 155 acres in 2002 and was shrinking at a rate of about 3% per year.
(a) Write a formula for the size, S, of the glacier, in acres, as a function of years tt since 2002.
S(t)=( )
(b) Use the model to predict the size of the glacier in the year 2009.
Size: ( ). acres
(c) According to the model, how many acres of ice were lost from the glacier between 2002 and 2008?
Acres lost: ( )
5) The amount (in milligrams) of a drug in the body tt hours after taking a pill is given by A(t)=35(0.85)^t
(a) What is the initial dose given?
Dose: ( )mg
(b) What percent of the drug leaves the body each hour?
Percent: ( )
(c) What is the amount of drug left after 9 hours?
Amount:( ) mg
(d) What is the first whole number of hours at which there is less than 4 milligrams left in the body?
Time:( ) hr
6) Find the exponential function f(x)=Ca^x whose graph goes through the points (0,5) and (3,40)
a=( )
C= ( )
7)The table below contain values from functions which each may be exponential or linear.
| xx | f(x)f(x) | g(x)g(x) |
| 00 | 15.515.5 | 33 |
| 11 | 1919 | 3.33.3 |
| 22 | 22.522.5 | 3.633.63 |
| 33 | 2626 | 3.9933.993 |
| 44 | 29.529.5 | 4.39234.3923 |
(a) Decide if each function is linear or exponential.
(b) Find a possible formula for each function.
f(x)= ( )
g(x)=( )
8) There were 8.65 million licensed drivers in Pennsylvania in 2009 and 8.43 million in 2004. Find a formula for the number, N, of licensed drivers in the US as a function oftt, the number of years since 2004, assuming growth is
(a) Linear
N(t)= ( ) million drivers
(b) Exponential
N(t)= ( ) million drivers
9) A town has a population of 12001200 people at time t=0t=0. In each of the following cases, write a formula for the population PP, of the town as a function of year tt.
(a) The population increases by 6060 people per year.
P= ( ) people
(b) The population increases by 11 percent a year.
P=( ) people
13) If 37600 dollars is invested at an interest rate of 9 percent per year, find the value of the investment at the end of 5 years for the following compounding methods.
(a) Annual:
(b) Semiannual:
(c) Monthly:
(d) Daily:
14) Your $8400 investment grows to $14000 over the course of 7 years compounded quarterly. What interest rate did you receive on your investment? (Write your answer with at least four decimal points)
Your interest rate is r=( )
15) Let P(t)=37(1−e^−kt)+53 represent the expected score for a student who studies tt hours for a test. Suppose k=0.43k=0.43 and test scores must be integers.
What is the highest score the student can expect?
If the student does not study, what score can he expect?
16) The number of bacteria in a culture is modeled by
where t is given in hours.
(a) The initial number of bacteria is
(b) The continuous rate of growth of this bacterium population is
(c) The hourly rate of growth of this bacterium population is
(d) The number of bacteria after 3 hours is
(e) After how many hours will the number of bacteria reach 10,000?
17) Find the initial value a, growth/decay factor b, and growth/decay rate r for the following exponential function:
(a) The initial value is a=( )
(b) The growth factor is b=( )
(c) The growth rate is r=( )%
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