[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.
Visit
this website for additional practice questions from Learningpod.
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.
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
