Concept explainers
Videos
(a)
To find: The linear model of the data.
(a)
Answer to Problem 31E
Explanation of Solution
Given:The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with
Using regression graphing calculator, the linear model of the above data is
The coefficient of determination is
Now plot the model and data on same window view.
(b)
To find: The power model of the data.
(b)
Answer to Problem 31E
Explanation of Solution
Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with
Using regression graphing calculator, the power model of the above data is
The coefficient of determination is
Now plot the model and data on same window view.
(c)
To find: The exponential model of the data.
(c)
Answer to Problem 31E
Explanation of Solution
Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with
Using regression graphing calculator, the exponential model of the above data is
The coefficient of determination is
Now plot the model and data on same window view.
(d)
To find: The logarithmic model of the data.
(d)
Answer to Problem 31E
Explanation of Solution
Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with
Using regression graphing calculator, the logarithmic model of the above data is
The coefficient of determination is
Now plot the model and data on same window view.
(e)
To find: The model which is best fit for data.
(e)
Answer to Problem 31E
Linear Model
Explanation of Solution
Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with
Linear model,
Power model,
Exponential model,
Logarithmic model,
The coefficient of determination of linear model is nearest 1.
So, Best fir model would be linear model.
(f)
To find: The population in year 2025 of each model.
(f)
Answer to Problem 31E
For linear model population in Jamaica is 3.014
For power model population in Jamaica is 2.909
For exponential model population in Jamaica is 3.024
For logarithmic model population in Jamaica is 2.908
Explanation of Solution
Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with
For 2025 corresponding value of
Put
Linear model,
Power model,
Exponential model,
Logarithmic model,
(g)
To predict: The best fir model for population in year 2025.
(g)
Answer to Problem 31E
Power model
Explanation of Solution
Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with
For 2025 corresponding value of
Put
Linear model,
Power model,
Exponential model,
Logarithmic model,
According to above calculation best model is power model.
(h)
To choose: The model different for different cases.
(h)
Answer to Problem 31E
No
Explanation of Solution
Given: The population P (in millions) of Jamacia for the years 2001 through 2016 are shown in the table, where t represents the year, with
For 2025 corresponding value of
Put
Linear model,
Power model,
Exponential model,
Logarithmic model,
According to above calculation best model is power model.
According to graph best model is linear because the coefficient of determination is nearest to 1 but according to calculation model is different because data may be vary.
Chapter 3 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- Coast Guard Patrol Search Mission The pilot of a Coast Guard patrol aircraft on a search mission had just spotted a disabled fishing trawler and decided to go in for a closer look. Flying in a straight line at a constant altitude of 1000 ft and at a steady speed of 256 ft/s, the aircraft passed directly over the trawler. How fast (in ft/s) was the aircraft receding from the trawler when it was 1400 ft from the trawler? (Round your answer to one decimal places.) 1000 ft 180 × ft/s Need Help? Read It SUBMIT ANSWERarrow_forward6. The largest interval in which the solution of (cos t)y′′ +t^2y′ − (5/t)y = e^t/(t−3) , y(1) = 2, y′(1) = 0is guaranteed to exist by the Existence and Uniqueness Theorem is:A. (0, ∞) B. (π/2, 3) C. (0,π/2) D. (0, π) E. (0, 3)arrow_forward12. For the differential equation in the previous question, what is the correct form for a particularsolution?A. yp = Ae^t + Bt^2 B. yp = Ae^t + Bt^2 + Ct + DC. yp = Ate^t + Bt^2 D. yp = Ate^t + Bt^2 + Ct + D Previous differential equation y′′ − 4y′ + 3y = e^t + t^2arrow_forward
- 16. The appropriate form for the particular solution yp(x) of y^(3) − y′′ − 2y′ = x^2 + e^2x isA. yp(x) = Ax^2 + Bx + C + De^2x B. yp(x) = Ax^3 + Bx^2 + Cx + Dxe^2xC. yp(x) = Ax^2 +Be^2x D. yp(x) = A+Be^2x +Ce^−x E. yp(x) = Ax^2 +Bx+C +(Dx+E)e^2xarrow_forwardDistance Between Two Ships Two ships leave the same port at noon. Ship A sails north at 17 mph, and ship B sails east at 11 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.) 20.3 X mph Need Help? Read It Watch It SUBMIT ANSWERarrow_forwardpractice problem please help!arrow_forward
- Find the first and second derivatives of the function. f(u) = √7 3u − 3 f'(u) 2 (7-34) (½) f"(u) = 9 4(7-3u) 32 X Need Help? Read It Watch It SUBMIT ANSWERarrow_forward11. Consider the 2nd-order non-homogeneous differential equation y′′ − 4y′ + 3y = et + t2What is the complementary (or homogeneous) solution?A. yc = c1e^t + c2t^2 B. yc = c1e^−t + c2e^−3t C. yc = c1e^t + c2e^3t D. yc = c1e^t + c2e^−3tarrow_forward5. A trial solution for the non-homogeneous equation y′′ + y′ − 2y = e^x isA. Ae^x B. Ae^x+ Be^−2x C. Ae^x + Be^−x D. Axe^x E. None of these.arrow_forward
- 14. Write u = - sint-cost in the form u = C cos(t - a) with C > 0 and 0 ? PAUSE Z X C VI B N Marrow_forward19. If the method of undetermined coefficients is used, the form of a particular solution ofy^(4) − y = e^−t + 3 sin(t) isA. yp(t) = Ate^−t + B cos(t) + C sin(t)B. yp(t) = At^2e^−t + B cos(t) + C sin(t)C. yp(t) = Ate^−t + Bt cos(t) + Ct sin(t)D. yp(t) = At^2e^−t + Bt cos(t) + Ct sin(t)E. yp(t) = Ate^−t + Bt sin(t)arrow_forward15. A spring-mass system is governed by the differential equation 2x′′ + 72x = 100 sin(3ωt) .For what value of ω will resonance occur?A. 3 B. 6√2 C. 2 D. 10 E. No valuearrow_forward
Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage Learning
Thomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. Freeman
Calculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning