<< Chapter < Page Chapter >> Page >

[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
  1. Let x represent time in years starting with x = 0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data.
  2. Use the model to predict the seal population for the year 2020.
  3. To the nearest whole number, what is the limiting value of this model?
  1. The logistic regression model that fits these data is y = 25.65665979 1 + 6.113686306 e 0.3852149008 x .
  2. If the population continues to grow at this rate, there will be about 25,634 seals in 2020.
  3. To the nearest whole number, the carrying capacity is 25,657.
Got questions? Get instant answers now!

Access this online resource for additional instruction and practice with exponential function models.

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 y = a b x 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 y = a + b ln ( x ) 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 y = c 1 + a e b x 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.

Got questions? Get instant answers now!

What is a carrying capacity? What kind of model has a carrying capacity built into its formula? Why does this make sense?

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Questions & Answers

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask