GP Unit 4wanda

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4) For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4. Round your answer to the nearest tenth’s place.

a) Show coordinates in this space

(0,1), (1,1.1), (2,1.2), (3,1.3), (4,1.5)

Show work in this space and explain your answer

A is the total amount after interest is calculated, P is the amount that was originally invested, r is the interest rate, and n is the compounding cycle.

P = 1, n = 1, r = .1 (Given)

So, at the beginning, t =0: Therefore, at the beginning, the total amount is equal to the initial investment.

After one time increment, A = 1.11, A=1.1. Therefore, after one time increment, the new total is 1.1 times the initial investment.

After two time increments, A = 1.12, A=1.21. Therefore, after two time increments, the new total is 1.121 times the initial investment. Rounding to the nearest tenth gives 1.2.

After three time increments, A = 1.13, A=1.331. Therefore, after three time increments, the new total is 1.331 times the initial investment. Rounding to the nearest tenth gives 1.3.

After four time increments, A = 1.14, A=1.4641. Therefore, after four time increments, the new total is 1.4641 times the initial investment. Rounding to the nearest tenth gives 1.5.

b) Show graph here

Note: The curve would be more visible if the coordinates had not been rounded.

5) Logarithms:

a) Using a calculator, find log 10000 where log means log to the base of 10.

Answer and explain it:

log10 10000 = 4. This means that 10000 is equivalent to 104.

b) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she uses a log to the base 2. To find the log of a number to any base, we can use a conversion formula as shown here:

Using this formula, find . Round your answer to the hundredth’s place.

Answer and explain it:

Log210000 = 13.29. This means that 10000 is equivalent to 213.29, rounded to the hundredth’s place.

Show work in this space

a = 10000, b = 2

The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear.

Using the Library, web resources, and other course material, research how sound is measured. Include the following items in your posting:

· The formula for measuring sound.

· Pick a specific sound, give the decibels of the sound, and explain what this measurement means.

The SI unit for sound level is the bel, named after Alexander Graham Bell (Giancoli 2005, p. 325).

The more common unit is the decibel, which is one tenth of a bel (Giancoli 2005, p. 325).

The formula for measuring sound is: Where ? is the sound level in decibels. I0 equals 1.0 X 10-12 watts/meter2. This is the minimum intensity that is audible to a “good” ear. So a sound that is barely audible would have an intensity of 0 dB (Giancoli 2005, p. 325).

An increase in intensity by a factor of 10 is an increase of 10 dB. But an increase in intensity by a factor of 100 is an increase of 20 dB. Thus a noise that has an intensity of 100 dB is 10 times as intense as a sound at 90 dB, but 100 times as intense as a sound at 80 dB (Giancoli 2005, p. 325).

A quiet radio has an intensity of 40 dB. This is 104 greater in intensity, or 10,000 times as intense, as the minimum intensity that is audible (Giancoli 2005, p. 325).

References

Giancoli, D. (2005). Physics. Upper Saddle River, NJ: Pearson Prentice Hall.

Be sure to cite all references using APA style. This important, I nee the references on where you found this information.