Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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Concept explainers
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.
Topic Video
Question
#3
![VTalking:
1.
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has
increased to 270.
(a) Find an expression for the number of bacteria after t hours.
P(t) =
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.)
P(2) =
bacteria
(c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.)
P'(2) =
bacteria per hour
(d) When will the population reach 10,000? (Round your answer to one decimal place.)
%3D
hr
Water is leaking out of an inverted conical tank at a rate of 7,000 cm3/min at the same time that water is being pumped into
the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of
20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. (Round your
2.
answer to the nearest integer.)
3.
Find the linearization L(x) of the function at a.
f(x) = Vx, a = 4
4.
(a) Find the differential dy.
y = ex/2
dy =
(b) Evaluate dy for the given values of x and dx.
X = 0,
dx = 0.05
dy =
5.
Compute Ay and dy for the given values of x and dx = Ax. (Round your answers to three decimal places.)
9:43 AM
O Type here to search
O 4)
IJ
4/7/2021
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc6ffd85-d0a1-4b45-ac73-1efaf2cd285f%2F447b5bf6-e32f-4358-bf96-de30ca92f88e%2F3dbyu4_processed.png&w=3840&q=75)
Transcribed Image Text:VTalking:
1.
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has
increased to 270.
(a) Find an expression for the number of bacteria after t hours.
P(t) =
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.)
P(2) =
bacteria
(c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.)
P'(2) =
bacteria per hour
(d) When will the population reach 10,000? (Round your answer to one decimal place.)
%3D
hr
Water is leaking out of an inverted conical tank at a rate of 7,000 cm3/min at the same time that water is being pumped into
the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of
20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. (Round your
2.
answer to the nearest integer.)
3.
Find the linearization L(x) of the function at a.
f(x) = Vx, a = 4
4.
(a) Find the differential dy.
y = ex/2
dy =
(b) Evaluate dy for the given values of x and dx.
X = 0,
dx = 0.05
dy =
5.
Compute Ay and dy for the given values of x and dx = Ax. (Round your answers to three decimal places.)
9:43 AM
O Type here to search
O 4)
IJ
4/7/2021
5
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