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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

A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply
circular region of radious
Kainat Reply
how can we solve this problem
Joel Reply
Sin(A+B) = sinBcosA+cosBsinA
Eseka Reply
Prove it
Eseka
Please prove it
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
Practice Key Terms 4

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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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