Refer a friend and earn $50 when they subscribe to an annual planRefer Now
Get the answer to your homework problem.
Try Numerade Free for 30 Days
Like
Report
Indian population The table gives the midyear population of India (in millions) for the last half of the 20th century.(a) Make a scatter plot, semilog plot, and log-log plot for these data and comment on which type of model would be most appropriate.(b) Obtain an exponential model for the population.(c) Use your model to estimate the population in 2010 and compare with the actual population of 1173 million. What conclusion can you make?
(a) See explanation for graphs; Exponential(b) $y=\left(2.2761 \cdot 10^{-15}\right)\left(1.02052861^{x}\right)$(c) 1247 million people; the model overestimates the population
Calculus 1 / AB
Chapter 1
Functions and Sequences
Section 5
Logarithms; Semilog and Log-Log Plots
Functions
Campbell University
Oregon State University
Baylor University
Lectures
03:09
In mathematics, precalculu…
31:55
In mathematics, a function…
13:16
The table gives the popula…
07:48
Population Growth In 2000 …
07:54
The table gives estimates …
10:07
World population The table…
12:25
16:06
02:34
The population of Delhi, I…
03:05
The population of Banglade…
04:01
The table shows the mid…
01:40
World Population Growth si…
first we must make a scatter plot semi log plot and log log plot for our data. So here I've done this in days most but you can use any graphing tool available to you. This is our base data, the plane data, just the year values and the population values in millions given to us. And so it makes this nice scatter plot here in black. Now for the semi log plot we have taken the base 10 logarithms of our population values and then plotted them against the plane year values. So now we have this blue semi log plot. And finally for the log log plot we used We took the base 10 logarithms of both the years and the population values. And so it gives us this nice red log log plot. Now to find the best model for our data, we can observe each of these plots and see how well they fit to align. If the linear, if the scatter plot fits best to align, then we should best use a linear model. But that does not seem to be the case here, as there's a little bit of a curve, as you can see in the semi log plot. If the semi log plot best fits to a line and we should use an exponential model, it does look pretty good if the log log plot fits best to headline, we should use a power model, but out of the three of these, the semi log plot appears to be the most linear. So we should use an exponential model for this data. Now we must generate the exponential model for this data. And so we can also do this in dez most. So here this is the data straight from the problem. This is also the data we used for the scatter plot problem. And so you can use Dismas to generate an exponential model, like. So it will give you the coefficients here in terms of A. And B. And so you can see that a is about 2.276, 1 Times 10 to the -15. And I forgot to write exponential his vest. Sorry about that. And then our B value is about 1.02053. If we round it off here 1.02053 for the final part of our problem, we have to estimate The population in 2010 using our model. So we plug in the coefficients we found in the last part And then plug in 2010 for X as our year. And if you plug this into your calculator and round up to the nearest million, you will get about 1,274 million people. And so compared to the actual population of 1,173 million people, Our models slightly overestimates. So from this we can deduce that our population will approximately overestimate the population for a given year, right a year.
View More Answers From This Book
Find Another Textbook
Numerade Educator
In mathematics, precalculus is the study of functions (as opposed to calculu…
In mathematics, a function (or map) f from a set X to a set Y is a rule whic…
The table gives the population of India, in millions, for thesecond half…
Population Growth In 2000 India's population reached 1 billion, and it …
The table gives estimates of the world population, in millions, from 1750 to…
World population The table gives estimates of the worldpopulation, in mi…
The table gives estimates of the world population, inmillions, from 1750…
The population of Delhi, India, can be modeled by$$P(t)=9817(1.031)^…
The population of Bangladesh was $153,000,000$ in 2009 with an annual growth…
The table shows the mid-year populations $ a_n $ of China (in million…
World Population Growth since 2000 , world population in millions closely fi…
01:19
Find $f$ . $f^{\prime}(x)=\sqrt{x}(6+5 x), \quad f(1)=10$
01:07
Find the most general antiderivative of the function.(Check your answer by d…
$59-62$ Produce graphs of $f$ that reveal all the important aspectsof th…
03:15
Evaluate the integral.$\int \ln \sqrt[3]{x} d x$
04:15
(a) Find $y^{\prime}$ by implicit differentiation.(b) Solve the equation…
00:37
Evaluate the indefinite integral.$\int x \sin \left(x^{2}\right) d x$
01:11
Evaluate the integral.$\int_{1}^{2}(1+2 y)^{2} d y$
14:58
Blood cell production $\mathrm{A}$ simple model of blood cell production is …
00:58
Use the form of the definition of the integral given inTheorem 4 to eval…
00:41
Evaluate the indefinite integral.$\int \frac{x}{1+x^{4}} d x$
92% of Numerade students report better grades.
Try Numerade Free for 30 Days. You can cancel at any time.
Annual
0.00/mo 0.00/mo
Billed annually at 0.00/yr after free trial
Monthly
0.00/mo
Billed monthly at 0.00/mo after free trial
Earn better grades with our study tools:
Textbooks
Video lessons matched directly to the problems in your textbooks.
Ask a Question
Can't find a question? Ask our 30,000+ educators for help.
Courses
Watch full-length courses, covering key principles and concepts.
AI Tutor
Receive weekly guidance from the world’s first A.I. Tutor, Ace.
30 day free trial, then pay 0.00/month
30 day free trial, then pay 0.00/year
You can cancel anytime
OR PAY WITH
Your subscription has started!
The number 2 is also the smallest & first prime number (since every other even number is divisible by two).
If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".
Receive weekly guidance from the world's first A.I. Tutor, Ace.
Mount Everest weighs an estimated 357 trillion pounds
Snapshot a problem with the Numerade app, and we'll give you the video solution.
A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.
Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.