Lead was banned as an ingredient in most paints in 1978, although it is still used in specialty paints. Lead usage in paints from 1940 through 1980 is reported in the accompanying table. Lead usage (thousands of tons) Year 1940 70 1950 35 1960 10 1970 5 1980 0.01 (a) Align the input data as years after 1940. Examine a scatter plot of the data. Find quadratic and exponential models for lead usage. (Round your coefficients to 3 decimal places.) Quadratic Model Q(x) = thousands of tons of lead was used in paints x years after 1940, for the years from 1940 through 1980. Exponential Model E(x) = thousands of tons of lead was used in paints x years after 1940, for the years from 1940 through 1980. (b) Based on how well each function fits the data, which model would be best for interpolating (estimating lead usage between 1940 and 1980). O The quadratic model would be best for interpolating because it fits the data better between 1940 and 1980. O Either model would work equally well for interpolating because they both fit the data well between 1940 and 1980. O The exponential model would be best for interpolating because it fits the data better between 1940 and 1980. (c) Based on the fact that lead was banned in most paints in 1978, which function would be best for extrapolating values for more recent years (estimating lead usage after 1980)? Why? O The quadratic model would best estimate the lead usage after 1980 because the graph approaches zero as you move farther to the right. O The quadratic model would best estimate the lead usage after 1980 because the graph approaches infinity as you move farther to the right. O The exponential model would best estimate the lead usage after 1980 because the graph approaches infinity as you move farther to the right. O The exponential model would best estimate the lead usage after 1980 because the graph approaches zero as you move farther to the right.
Lead was banned as an ingredient in most paints in 1978, although it is still used in specialty paints. Lead usage in paints from 1940 through 1980 is reported in the accompanying table. Lead usage (thousands of tons) Year 1940 70 1950 35 1960 10 1970 5 1980 0.01 (a) Align the input data as years after 1940. Examine a scatter plot of the data. Find quadratic and exponential models for lead usage. (Round your coefficients to 3 decimal places.) Quadratic Model Q(x) = thousands of tons of lead was used in paints x years after 1940, for the years from 1940 through 1980. Exponential Model E(x) = thousands of tons of lead was used in paints x years after 1940, for the years from 1940 through 1980. (b) Based on how well each function fits the data, which model would be best for interpolating (estimating lead usage between 1940 and 1980). O The quadratic model would be best for interpolating because it fits the data better between 1940 and 1980. O Either model would work equally well for interpolating because they both fit the data well between 1940 and 1980. O The exponential model would be best for interpolating because it fits the data better between 1940 and 1980. (c) Based on the fact that lead was banned in most paints in 1978, which function would be best for extrapolating values for more recent years (estimating lead usage after 1980)? Why? O The quadratic model would best estimate the lead usage after 1980 because the graph approaches zero as you move farther to the right. O The quadratic model would best estimate the lead usage after 1980 because the graph approaches infinity as you move farther to the right. O The exponential model would best estimate the lead usage after 1980 because the graph approaches infinity as you move farther to the right. O The exponential model would best estimate the lead usage after 1980 because the graph approaches zero as you move farther to the right.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Concept explainers
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
Question
Transcribed Image Text:Modeling Review
Lead was banned as an ingredient in most paints in 1978, although it is still used in specialty paints. Lead usage in paints from 1940 through 1980 is reported in
the accompanying table.
Lead usage
(thousands of tons)
Year
1940
70
1950
35
1960
10
1970
5
1980
0.01
(a) Align the input data as years after 1940. Examine a scatter plot of the data. Find quadratic and exponential models for lead usage. (Round your
coefficients to 3 decimal places.)
Quadratic Model
Q(x) =
thousands of tons of lead was used in paints x years after 1940, for the years from 1940 through 1980.
Exponential Model
E(x) =
thousands of tons of lead was used in paints x years after 1940, for the years from 1940 through 1980.
(b) Based on how well each function fits the data, which model would be best for interpolating (estimating lead usage between 1940 and 1980).
O The quadratic model would be best for interpolating because it fits the data better between 1940 and 1980.
O Either model would work equally well for interpolating because they both fit the data well between 1940 and 1980.
O The exponential model would be best for interpolating because it fits the data better between 1940 and 1980.
(c) Based on the fact that lead was banned in most paints in 1978, which function would be best for extrapolating values for more recent years (estimating
lead usage after 1980)? Why?
O The quadratic model would best estimate the lead usage after 1980 because the graph approaches zero as you move farther to the right.
O The quadratic model would best estimate the lead usage after 1980 because the graph approaches infinity as you move farther to the right.
O The exponential model would best estimate the lead usage after 1980 because the graph approaches infinity as you move farther to the right.
O The exponential model would best estimate the lead usage after 1980 because the graph approaches zero as you move farther to the right.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
