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x 1 2 3 4
f ( x ) 70 40 10 -20

Linear

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x 1 2 3 4
h ( x ) 70 49 34.3 24.01
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x 1 2 3 4
m ( x ) 80 61 42.9 25.61

Neither

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x 1 2 3 4
f ( x ) 10 20 40 80
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x 1 2 3 4
g ( x ) -3.25 2 7.25 12.5

Linear

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For the following exercises, use the compound interest formula, A ( t ) = P ( 1 + r n ) n t .

After a certain number of years, the value of an investment account is represented by the equation 10 , 250 ( 1 + 0.04 12 ) 120 . What is the value of the account?

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What was the initial deposit made to the account in the previous exercise?

$ 10 , 250

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How many years had the account from the previous exercise been accumulating interest?

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An account is opened with an initial deposit of $6,500 and earns 3.6 % interest compounded semi-annually. What will the account be worth in 20 years?

$ 13 , 268.58

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How much more would the account in the previous exercise have been worth if the interest were compounding weekly?

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Solve the compound interest formula for the principal, P .

P = A ( t ) ( 1 + r n ) n t

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Use the formula found in the previous exercise to calculate the initial deposit of an account that is worth $ 14 , 472.74 after earning 5.5 % interest compounded monthly for 5 years. (Round to the nearest dollar.)

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How much more would the account in the previous two exercises be worth if it were earning interest for 5 more years?

$ 4,572.56

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Use properties of rational exponents to solve the compound interest formula for the interest rate, r .

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Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $9,000 and was worth $13,373.53 after 10 years.

4 %

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Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded monthly, had an initial deposit of $5,500, and was worth $38,455 after 30 years.

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

y = 3742 ( e ) 0.75 t

continuous growth; the growth rate is greater than 0.

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y = 2.25 ( e ) 2 t

continuous decay; the growth rate is less than 0.

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Suppose an investment account is opened with an initial deposit of $ 12 , 000 earning 7.2 % interest compounded continuously. How much will the account be worth after 30 years?

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How much less would the account from Exercise 42 be worth after 30 years if it were compounded monthly instead?

$ 669.42

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Numeric

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.

f ( x ) = 2 ( 5 ) x , for f ( 3 )

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f ( x ) = 4 2 x + 3 , for f ( 1 )

f ( 1 ) = 4

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f ( x ) = e x , for f ( 3 )

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f ( x ) = 2 e x 1 , for f ( 1 )

f ( 1 ) 0.2707

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f ( x ) = 2.7 ( 4 ) x + 1 + 1.5 , for f ( 2 )

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f ( x ) = 1.2 e 2 x 0.3 , for f ( 3 )

f ( 3 ) 483.8146

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f ( x ) = 3 2 ( 3 ) x + 3 2 , for f ( 2 )

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Technology

For the following exercises, use a graphing calculator to find the equation of an exponential function given the points on the curve.

( 0 , 3 ) and ( 3 , 375 )

y = 3 5 x

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( 3 , 222.62 ) and ( 10 , 77.456 )

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( 20 , 29.495 ) and ( 150 , 730.89 )

y 18 1.025 x

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( 5 , 2.909 ) and ( 13 , 0.005 )

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( 11,310.035 ) and ( 25,356.3652 )

y 0.2 1.95 x

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Extensions

The annual percentage yield (APY) of an investment account is a representation of the actual interest rate earned on a compounding account. It is based on a compounding period of one year. Show that the APY of an account that compounds monthly can be found with the formula APY = ( 1 + r 12 ) 12 1.

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Questions & Answers

what is mutation
Janga Reply
what is a cell
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how is urine form
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mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
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how many types of solid did we have
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What is Atoms
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what is bladder
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urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
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how is urine formed in human
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how is urine formed in human
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what is the diference between a cavity and a canal
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what is the causative agent of malaria
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malaria is caused by an insect called mosquito.
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Malaria is cause by female anopheles mosquito
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Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
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a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
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respiration is the process in which we breath in oxygen and breath out carbon dioxide
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how are lungs work
Commander
where does digestion begins
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in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
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stimulates the follicle to release the mature ovum into the oviduct
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what are the functions of Endocrine and pituitary gland
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endocrine secrete hormone and regulate body process
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while pituitary gland is an example of endocrine system and it's found in the Brain
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what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
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biology is the study of life.
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Biology is the study of how living organisms live and survive in a specific environment
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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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