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- Exponential and logarithmic
- Fitting exponential models to
Use a graphing utility to find an exponential regression formula
and a logarithmic regression formula
for the points
and
Round all numbers to 6 decimal places. Graph the points and both formulas along with the line
on the same axis. Make a conjecture about the relationship of the regression formulas.
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Verify the conjecture made in the previous exercise. Round all numbers to six decimal places when necessary.
First rewrite the exponential with base
e :
Then test to verify that
taking rounding error into consideration:
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Use the result from the previous exercise to graph the logistic model
along with its inverse on the same axis. What are the intercepts and asymptotes of each function?
The graph of
has a
y -intercept at (0, 4) and horizontal asymptotes at
y = 0 and
y = 20. The graph of
has an
x - intercept at (4, 0) and vertical asymptotes at
x = 0 and
x = 20.
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Chapter review exercises
Determine whether the function
represents exponential growth, exponential decay, or neither. Explain
exponential decay; The growth factor,
is between
and
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The population of a herd of deer is represented by the function
where
is given in years. To the nearest whole number, what will the herd population be after
years?
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Determine whether
[link] could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.
x |
1 |
2 |
3 |
4 |
f(x) |
3 |
0.9 |
0.27 |
0.081 |
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Hsu-Mei wants to save $5,000 for a down payment on a car. To the nearest dollar, how much will she need to invest in an account now with
APR, compounded daily, in order to reach her goal in
years?
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Suppose an investment account is opened with an initial deposit of
earning
interest, compounded continuously. How much will the account be worth after
years?
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Graph the function
State the domain and range and give the
y -intercept.
domain: all real numbers; range: all real numbers strictly greater than zero;
y -intercept: (0, 3.5);
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The graph of
is reflected about the
y -axis and stretched vertically by a factor of
What is the equation of the new function,
State its
y -intercept, domain, and range.
y -intercept:
Domain: all real numbers; Range: all real numbers greater than
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Questions & Answers
how does the planets on our solar system orbit
how many Messier objects are there in space
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
Roaul
I want to be an astronomer. That's my dream
Astrit
Who named the the whole galaxy?
what is the dark matter
Richard
what are the factors upon which the atmosphere is stratified
bigbang is the beginning of the universe
Sokak
but thats just a theory
Sokak
nothing will happen, don't worry brother.
Vansh
these are Rocky substances between mars and jupiter
GANGAIN
Comets are cosmic snowballs of frozen gases , rock and dust that orbit the sun. They are mostly found between the orbits of Venus and Mercury.
Aarya
hey can anyone guide me abt international astronomy olympiad
sahil
how can we learn right and true ?
why the moon is always appear in an elliptical shape
Because when astroid hit the Earth then a piece of elliptical shape of the earth was separated which is now called moon.
Hemen
Did you mean eye sight or sea level
Minal
oh sorry it's sea level
lidiya
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
w astronomy and cosmology!
Michele
another theory of universe except big ban
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
I think it couldn't possible on earth
Nagalakshmi
in this time i don't Know
Michele
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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