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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

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
the polar co-ordinate of the point (-1, -1)
Sumit Reply
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
B=Ai-itan(hx-hiy)
Rukmini
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana Reply
the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success 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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