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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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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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