[link] shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012.
Year
Seal Population (Thousands)
Year
Seal Population (Thousands)
1997
3.493
2005
19.590
1998
5.282
2006
21.955
1999
6.357
2007
22.862
2000
9.201
2008
23.869
2001
11.224
2009
24.243
2002
12.964
2010
24.344
2003
16.226
2011
24.919
2004
18.137
2012
25.108
Let
represent time in years starting with
for the year 1997. Let
represent the number of seals in thousands. Use logistic regression to fit a model to these data.
Use the model to predict the seal population for the year 2020.
To the nearest whole number, what is the limiting value of this model?
The logistic regression model that fits these data is
If the population continues to grow at this rate, there will be about
seals in 2020.
To the nearest whole number, the carrying capacity is 25,657.
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Key concepts
Exponential regression is used to model situations where growth begins slowly and then accelerates rapidly without bound, or where decay begins rapidly and then slows down to get closer and closer to zero.
We use the command “ExpReg” on a graphing utility to fit function of the form
to a set of data points. See
[link] .
Logarithmic regression is used to model situations where growth or decay accelerates rapidly at first and then slows over time.
We use the command “LnReg” on a graphing utility to fit a function of the form
to a set of data points. See
[link] .
Logistic regression is used to model situations where growth accelerates rapidly at first and then steadily slows as the function approaches an upper limit.
We use the command “Logistic” on a graphing utility to fit a function of the form
to a set of data points. See
[link] .
Section exercises
Verbal
What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.
Logistic models are best used for situations that have limited values. For example, populations cannot grow indefinitely since resources such as food, water, and space are limited, so a logistic model best describes populations.
What is regression analysis? Describe the process of performing regression analysis on a graphing utility.
Regression analysis is the process of finding an equation that best fits a given set of data points. To perform a regression analysis on a graphing utility, first list the given points using the STAT then EDIT menu. Next graph the scatter plot using the STAT PLOT feature. The shape of the data points on the scatter graph can help determine which regression feature to use. Once this is determined, select the appropriate regression analysis command from the STAT then CALC menu.
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
