Question

This is the continuation of the question I have asked previously:

d. find the logarithmic model. Use one of these equations as your base: y1~alog(x1)+k or y1~aln(x1)+k. Then write down the best fit curve for the data.
4. a. Where on your radio dial would you find a station with a frequency of 93.3? Show work to justify your answer.
b. If you turned the radio dial to be 4 centimeters from the left end of the radio, what radio station would you pick up? Show work to justify your answer.

Answer 1

d. The logarithmic model can be expressed as y1~alog(x1)+k or y1~aln(x1)+k.

The best fit curve for the given data would be: y1 = 0.2 * log(x1) + k or y1 = 0.2 * ln(x1) + k

a. If you wanted to find a station with a frequency of 93.3 on your radio dial, you would need to use the formula Frequency = 88 + 0.2 * (Channel Number). Using this formula, we can calculate that the channel number for a frequency of 93.3 is:

Channel Number = (Frequency - 88) / 0.2

Channel Number = (93.3 - 88) / 0.2

Channel Number = 5.3

Therefore, a station with a frequency of 93.3 can be found on channel 5.3 on your radio dial.

b. If you turned the radio dial to be 4 centimeters from the left end of the radio, the channel number would be:

Channel Number = 4 / 0.2

Channel Number = 20

Using the formula Frequency = 88 + 0.2 * (Channel Number), we can calculate that the frequency for channel 20 is:

Frequency = 88 + 0.2 * (Channel Number)

Frequency = 88 + 0.2 * (20)

Frequency = 96.0

Therefore, turning the radio dial to be 4 centimeters from the left end of the radio, you will pick up a station with a frequency of 96.0.