Reminder Round all answers to two decimal places unless otherwise indicated.
A Violin String A violin string is stopped so that the resulting string length makes a desired musical note. In order to make the next higher note, the string must be shortened using a factor of
a. Find a formula for an exponential function that gives the length
b. One of the unstopped strings makes an
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- Richter Scale The Richter scale provides a measure of the magnitude of an earthquake. In fact, the largest Richter number M ever recorded for an earthquake was 8.9 from the 1933 earthquake in Japan. The following formula shows a relationship between the amount of energy released and the Richter number. M=23logE0.007, Where E is measured in kilowatt-hours. Source: Mathematics Teacher. a. For the 1933 earthquake in Japan, what value of E gives a Richter number M=8.9?. b. If the average household uses 247 kWh per month, how many months would the energy released by an earthquake of this magnitude power 10 million household? c. Find the rate of change of the Richter number M with respect to energy when E=70,000 kWh. d. What happens to dM/dE as E increases?arrow_forwardFalling with a Parachute If an average-sized man with parachute jumps an airplane, he will fall 12.50.2t 1 20t feet in t seconds. How long will it take him to fall 140 feet?arrow_forwardA Skydiver If a skydiver jumps from an airplane, his velocity v, in feet per second, starts at 0 and increases towards terminal velocity, an average-sized man has a terminal T of about 176 feet per second. The difference D=Tv is an exponential function of time, a. What is the initial value of D? b. Two second into fall, the velocity is 54.75 feet per seconds. Find an exponential formula for D. c. Find a formula for v. d. Express the velocity 4 seconds into the fall using functional notation, and then calculate that value.arrow_forward
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