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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

sinx sin2x is linearly dependent
cr Reply
what is a reciprocal
Ajibola Reply
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
 Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
Funmilola Reply
I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
sinx sin2x is linearly dependent
cr
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
Wrong question
Saad
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
what is the value of x in 4x-2+3
Vishal Reply
give the complete question
Shanky
4x=3-2 4x=1 x=1+4 x=5 5x
Olaiya
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0 then 4x = 2-3 4x = -1 x = -(1÷4) is the answer.
Jacob
4x-2+3 4x=-3+2 4×=-1 4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3 4x=-3+2 4x=-1 4x÷4=-1÷4 x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was  1350  bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?
David Reply
f(x)= 1350. 2^(t/20); where t is in hours.
Merkeb

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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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