Question 142770: We just started Log word problems,could you help me with a couple I'm having trouble with?
1) This one is titled Compound Interest
How much more interest could $500 earn in 5 years, compounded semiannually, if the annual interest rate were 5 1/2% instead of 5%?
2)This one is titled Decibel Voltage Gain
An amplifier produces an output of 17 volts when the input signal is 0.03 volt. Find the decibel voltage gain.
3)This one is titled Population Doubling Time
A town's population grows at the rate of 12% per year. If this growth rate remains constant, how long will it take the population to double?
4)This one is titled Population Doubling Time
How ling will it take the population of the town in problem #3 to triple?
5)This one is titled Richter Scale
An earthquake with a period of 1/4 second has an amplitude of 2,500 micrometers.Find its measure on the Richter scale.
Thank you in advance.I'm not good with word problems,but I'm glad that there are people like you that can help me understand them. Elle J
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1) This one is titled Compound Interest
How much more interest could $500 earn in 5 years, compounded semiannually, if the annual interest rate were 5 1/2% instead of 5%?
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At 5%: A(5) = 500(1+ (0.05)/2)^(2*5) = 640.04
Amt. of interest = 640.04 -500 = $140.04
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At 5.5%: A(5) = 500(1+ (0.055/2))^(10) = 655.83
Amt of interest = 655.83 -500 = $155.83
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Interest difference: 155.83-140.04 = $15.79
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2)This one is titled Decibel Voltage Gain
An amplifier produces an output of 17 volts when the input signal is 0.03 volt. Find the decibel voltage gain.
vg = 10log[17/0.03] = 10log[566.67] = 27.533 dB
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3)This one is titled Population Doubling Time
A town's population grows at the rate of 12% per year. If this growth rate remains constant, how long will it take the population to double?
A(t) = Ao(1.12^t)
2Ao = Ao*(1.12)^t
2 = 1.12^t
tlog1.12 = log2
t = log2/log1.12 = 6.116 years
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4)This one is titled Population Doubling Time
How long will it take the population of the town in problem #3 to triple?
3 = 1.12^t
t = log3/log1.12 = 9.694... years.
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5)This one is titled Richter Scale
An earthquake with a period of 1/4 second has an amplitude of 2,500 micrometers.Find its measure on the Richter scale.
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You may have a worked problem in your text that shows the formula
for calculating the magnitude when you know the amplitude and the
period of the wave.
You should include that formula in your posting.
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cheers,
Stan H.
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