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What might a scatterplot of data points look like if it were best described by a logarithmic model?

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What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?

The y -intercept on the graph of a logistic equation corresponds to the initial population for the population model.

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Graphical

For the following exercises, match the given function of best fit with the appropriate scatterplot in [link] through [link] . Answer using the letter beneath the matching graph.

Graph of a scattered plot.
Graph of a scattered plot.
Graph of a scattered plot.
Graph of a scattered plot.
Graph of a scattered plot.

y = 10.209 e 0.294 x

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y = 5.598 1.912 ln ( x )

C

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y = 4.607 + 2.733 ln ( x )

B

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y = 14.005 1 + 2.79 e 0.812 x

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Numeric

To the nearest whole number, what is the initial value of a population modeled by the logistic equation P ( t ) = 175 1 + 6.995 e 0.68 t ? What is the carrying capacity?

P ( 0 ) = 22 ; 175

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Rewrite the exponential model A ( t ) = 1550 ( 1.085 ) x as an equivalent model with base e . Express the exponent to four significant digits.

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A logarithmic model is given by the equation h ( p ) = 67.682 5.792 ln ( p ) . To the nearest hundredth, for what value of p does h ( p ) = 62 ?

p 2.67

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A logistic model is given by the equation P ( t ) = 90 1 + 5 e 0.42 t . To the nearest hundredth, for what value of t does P ( t ) = 45 ?

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What is the y -intercept on the graph of the logistic model given in the previous exercise?

y -intercept: ( 0 , 15 )

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Technology

For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P ( x ) = 68 1 + 16 e 0.28 x .

Graph the population model to show the population over a span of 3 years.

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What was the initial population of koi?

4 koi

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How many koi will the pond have after one and a half years?

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How many months will it take before there are 20 koi in the pond?

about 6.8 months.

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Use the intersect feature to approximate the number of months it will take before the population of the pond reaches half its carrying capacity.

Graph of the intersection of P(t)=68/(1+16e^(-0.28t)) and y=34.
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For the following exercises, use this scenario: The population P of an endangered species habitat for wolves is modeled by the function P ( x ) = 558 1 + 54.8 e 0.462 x , where x is given in years.

Graph the population model to show the population over a span of 10 years.

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What was the initial population of wolves transported to the habitat?

10 wolves

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How many wolves will the habitat have after 3 years?

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How many years will it take before there are 100 wolves in the habitat?

about 5.4 years.

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Use the intersect feature to approximate the number of years it will take before the population of the habitat reaches half its carrying capacity.

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For the following exercises, refer to [link] .

x f(x)
1 1125
2 1495
3 2310
4 3294
5 4650
6 6361

Use a graphing calculator to create a scatter diagram of the data.

Graph of the table’s values.
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Use the regression feature to find an exponential function that best fits the data in the table.

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Write the exponential function as an exponential equation with base e .

f ( x ) = 776.682 e 0.3549 x

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Graph the exponential equation on the scatter diagram.

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Use the intersect feature to find the value of x for which f ( x ) = 4000.

When f ( x ) = 4000 , x 4.6.

Graph of the intersection of a scattered plot with an estimation line and y=4,000.
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For the following exercises, refer to [link] .

x f(x)
1 555
2 383
3 307
4 210
5 158
6 122

Use a graphing calculator to create a scatter diagram of the data.

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Questions & Answers

x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0
HERVE Reply
x exposent4+4x exposent3+8x exposent2+4x+1=0
HERVE
How can I solve for a domain and a codomains in a given function?
Oliver Reply
ranges
EDWIN
Thank you I mean range sir.
Oliver
proof for set theory
Kwesi Reply
don't you know?
Inkoom
find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad
Martina Reply
factoring polynomial
Noven Reply
what's your topic about?
Shin Reply
find general solution of the Tanx=-1/root3,secx=2/root3
Nani Reply
find general solution of the following equation
Nani
the value of 2 sin square 60 Cos 60
Sanjay Reply
0.75
Lynne
0.75
Inkoom
when can I use sin, cos tan in a giving question
duru Reply
depending on the question
Nicholas
I am a carpenter and I have to cut and assemble a conventional roof line for a new home. The dimensions are: width 30'6" length 40'6". I want a 6 and 12 pitch. The roof is a full hip construction. Give me the L,W and height of rafters for the hip, hip jacks also the length of common jacks.
John
I want to learn the calculations
Koru Reply
where can I get indices
Kojo Reply
I need matrices
Nasasira
hi
Raihany
Hi
Solomon
need help
Raihany
maybe provide us videos
Nasasira
about complex fraction
Raihany
Hello
Cromwell
a
Amie
What do you mean by a
Cromwell
nothing. I accidentally press it
Amie
you guys know any app with matrices?
Khay
Ok
Cromwell
Solve the x? x=18+(24-3)=72
Leizel Reply
x-39=72 x=111
Suraj
Solve the formula for the indicated variable P=b+4a+2c, for b
Deadra Reply
Need help with this question please
Deadra
b=-4ac-2c+P
Denisse
b=p-4a-2c
Suddhen
b= p - 4a - 2c
Snr
p=2(2a+C)+b
Suraj
b=p-2(2a+c)
Tapiwa
P=4a+b+2C
COLEMAN
b=P-4a-2c
COLEMAN
like Deadra, show me the step by step order of operation to alive for b
John
A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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