logarithmic applications

The magnitude of an earthquake is calculated using the Richter Scale,M=logII/IoI , where I0 is the threshold intensity and the intensity I is given in terms of multiples of that threshold intensity. Which is the correct expression to find the magnitude of an earthquake that had the intensity 980 times the threshold intensity?

log(980)

Logarithmic and exponential functions are used in which of the following areas?

Physical science Electronics Social sciences business

Solve this application using logarithms. How much principal, to the nearest dollar, should you invest at 4% in order to have $3,000 for a vacation to Europe in 3 years? ≈ $

2.666.99

Solve this application using logarithms. How long will money in savings take to double at 5% interest compounded annually? Round the answer to the nearest hundredth of a year.

14.21 years

Solve this application using logarithms. At what interest rate (to the nearest hundredth of a percent) compounded annually will money in savings double in five years?

14.87

Solve this application using logarithms. At his son's birth, a man invested $2,000 in savings at 6% for his son's college education. Approximately how much, to the nearest dollar, will be available in 19 years? ≈ $ At his son's birth, a man invested $2,000 in a mutual fund earning 6.5% for his son's college education. Approximately how much, to the nearest dollar, will be available in 19 years? real value ≈ $ For each of the man's investments described above, how many years will it take for each investment to double in value? Round your answers to the nearest whole year. years to double savings account years to double mutual fund

6,051 6,617 12 11

The sound intensity of a typical vacuum cleaner is 80 dB (decibels). Sound intensity of 160 dB will burst an eardrum. How many times louder is the sound that will burst an eardrum than the sound of a vacuum cleaner?

Ten thousand times as loud.

The value of a car after t years can be found using the formula V = C(1 - r)t, where V is the current value of the car, C is the original price of the car, and r is the rate of depreciation. Solve the formula for r . Raj bought a car 4.5 years ago for $25,000, and the current value of the car is $12,000. At what percentage rate has the car depreciated? Round your answer to the nearest whole number.

V=C(1-r)^t (raise it to the t power) 12,000=25,000(1-r)^4.5 12000=25000(1-r)^4.5 (12000/25000) = (1-r)^4.5 0.48=(1-r)^4.5 logs of both sides log 0.48= -0.319=4.5 log (1-r) (-0.319/4.5)= -.0701=log(1-r) Now raise each to the 10 power 0.8495=1-r r= 0.1505 or 15.05%