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Algebraic

For the following exercises, identify whether the statement represents an exponential function. Explain.

The average annual population increase of a pack of wolves is 25.

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A population of bacteria decreases by a factor of 1 8 every 24 hours.

exponential; the population decreases by a proportional rate. .

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The value of a coin collection has increased by 3.25 % annually over the last 20 years.

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For each training session, a personal trainer charges his clients $ 5 less than the previous training session.

not exponential; the charge decreases by a constant amount each visit, so the statement represents a linear function. .

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The height of a projectile at time t is represented by the function h ( t ) = 4.9 t 2 + 18 t + 40.

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For the following exercises, consider this scenario: For each year t , the population of a forest of trees is represented by the function A ( t ) = 115 ( 1.025 ) t . In a neighboring forest, the population of the same type of tree is represented by the function B ( t ) = 82 ( 1.029 ) t . (Round answers to the nearest whole number.)

Which forest’s population is growing at a faster rate?

The forest represented by the function B ( t ) = 82 ( 1.029 ) t .

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Which forest had a greater number of trees initially? By how many?

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Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 20 years? By how many?

After t = 20 years, forest A will have 43 more trees than forest B.

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Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 100 years? By how many?

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Discuss the above results from the previous four exercises. Assuming the population growth models continue to represent the growth of the forests, which forest will have the greater number of trees in the long run? Why? What are some factors that might influence the long-term validity of the exponential growth model?

Answers will vary. Sample response: For a number of years, the population of forest A will increasingly exceed forest B, but because forest B actually grows at a faster rate, the population will eventually become larger than forest A and will remain that way as long as the population growth models hold. Some factors that might influence the long-term validity of the exponential growth model are drought, an epidemic that culls the population, and other environmental and biological factors.

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For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.

y = 220 ( 1.06 ) x

exponential growth; The growth factor, 1.06 , is greater than 1.

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y = 11 , 701 ( 0.97 ) t

exponential decay; The decay factor, 0.97 , is between 0 and 1.

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For the following exercises, find the formula for an exponential function that passes through the two points given.

( 0 , 6 ) and ( 3 , 750 )

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( 0 , 2000 ) and ( 2 , 20 )

f ( x ) = 2000 ( 0.1 ) x

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( 1 , 3 2 ) and ( 3 , 24 )

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( 2 , 6 ) and ( 3 , 1 )

f ( x ) = ( 1 6 ) 3 5 ( 1 6 ) x 5 2.93 ( 0.699 ) x

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( 3 , 1 ) and ( 5 , 4 )

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For the following exercises, determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.

Questions & Answers

For each year t, the population of a forest of trees is represented by the function A(t) = 117(1.029)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 86(1.025)t.
Shakeena Reply
by how many trees did forest "A" have a greater number?
Shakeena
32.243
Kenard
how solve standard form of polar
Rhudy Reply
what is a complex number used for?
Drew Reply
It's just like any other number. The important thing to know is that they exist and can be used in computations like any number.
Steve
I would like to add that they are used in AC signal analysis for one thing
Scott
Good call Scott. Also radar signals I believe.
Steve
Is there any rule we can use to get the nth term ?
Anwar Reply
how do you get the (1.4427)^t in the carp problem?
Gabrielle Reply
A hedge is contrusted to be in the shape of hyperbola near a fountain at the center of yard.the hedge will follow the asymptotes y=x and y=-x and closest distance near the distance to the centre fountain at 5 yards find the eqution of the hyperbola
ayesha Reply
A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. To the nearest hour, what is the half-life of the drug?
Sandra Reply
Find the domain of the function in interval or inequality notation f(x)=4-9x+3x^2
prince Reply
hello
Jessica Reply
Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the high temperature of ?105°F??105°F? occurs at 5PM and the average temperature for the day is ?85°F.??85°F.? Find the temperature, to the nearest degree, at 9AM.
Karlee Reply
if you have the amplitude and the period and the phase shift ho would you know where to start and where to end?
Jean Reply
rotation by 80 of (x^2/9)-(y^2/16)=1
Garrett Reply
thanks the domain is good but a i would like to get some other examples of how to find the range of a function
bashiir Reply
what is the standard form if the focus is at (0,2) ?
Lorejean Reply
a²=4
Roy Reply
Practice Key Terms 4

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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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