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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

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

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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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