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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

prove sin²x+cos²x=3+cos4x
Kiddy Reply
the difference between two signed numbers is -8.if the minued is 5,what is the subtrahend
jeramie Reply
the difference between two signed numbers is -8.if the minuend is 5.what is the subtrahend
jeramie
what are odd numbers
micheal Reply
numbers that leave a remainder when divided by 2
Thorben
1,3,5,7,... 99,...867
Thorben
7%2=1, 679%2=1, 866245%2=1
Thorben
the third and the seventh terms of a G.P are 81 and 16, find the first and fifth terms.
Suleiman Reply
if a=3, b =4 and c=5 find the six trigonometric value sin
Martin Reply
ask
Ans
pls how do I factorize x⁴+x³-7x²-x+6=0
Gift Reply
in a function the input value is called
Rimsha Reply
how do I test for values on the number line
Modesta Reply
if a=4 b=4 then a+b=
Rimsha Reply
a+b+2ab
Kin
commulative principle
DIOSDADO
a+b= 4+4=8
Mimi
If a=4 and b=4 then we add the value of a and b i.e a+b=4+4=8.
Tariq
what are examples of natural number
sani Reply
an equation for the line that goes through the point (-1,12) and has a slope of 2,3
Katheryn Reply
3y=-9x+25
Ishaq
show that the set of natural numberdoes not from agroup with addition or multiplication butit forms aseni group with respect toaaddition as well as multiplication
Komal Reply
x^20+x^15+x^10+x^5/x^2+1
Urmila Reply
evaluate each algebraic expression. 2x+×_2 if ×=5
Sarch Reply
if the ratio of the root of ax+bx+c =0, show that (m+1)^2 ac =b^2m
Awe 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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