Logarithmic Applications

An amount of $2,000 is deposited into a bank paying an annual interest rate of 2.85% compounded continuously. How long will it take for the money to double?

• 21.22 years
• 24.321 years
• 20.12 years
• Not here

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CCSS.HSF.LE.A.4

Caffeine leaves the body at a rate of 10% each hour. If I drank coffee at 9:00AM which has 95 mg of caffeine, when will I have half the amount left?

• after 6.58 hours
• after 7.27 hours
• after 6.89 hours
• not here

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CCSS.HSF.LE.A.4

You invest $5,000 into a savings account that has an interest rate of 5% compounded continuously. In how many years will there be $12000 in the account?

• 12.375 Years

• 177.073 Years

• 0.175 Years

• 17.509 Years

Decibels (dB) are defined by the equation; 10log [ I / I_o ] , where I_o = 10⁻¹² , the intensity of a barely audible sound. Use the formula to determine the loudness in dB of a jackhammer, which measures an intensity of 10⁻² .

• -10 dB

• 10 dB

• 20 dB

• 100 dB

If there are initially 2200 bacteria in a culture, and the number of bacteria triple each hour, the number of bacteria after t hours can be found using the formula y = 2200(3)^t . How long will it take the culture to grow to 60,000 bacteria?

• 1.52 hours

• 3.01 hours

• 4.25 hours

• 5.06 hours

Tags

CCSS.HSF.LE.A.4

In 1935 Charles Richter defined the magnitude of earthquakes to be M = log [I / s] where I is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicenter of the earthquake) and S is the intensity of a "standard earthquake" (whose amplitude is 1 micron equal to 10^-4 cm). In 1985

What is the magnitude of an earthquake with a seismographic reading of 79432 cm (when measured 100 km from the epicenter) rounded to the nearest tenth?

• 1.2

• 5.5

• 8.1

• 8.9

Use the mathematical model for power gain: G = log [P_o / P_i ]¹⁰ where P_o is the output power in watts and P_i is the input power in watts. Determine the power gain G in decibels, for an amplifier with an output P_o of 20 watts and an input P_i of 1.6 watts. Round to five decimal places if necessary.

• 11.9691 dB

• 10.9691 dB

• 15.0515 dB

• 12.64818 dB

What is the magnitude of an earthquake with a seismographic reading of 63 cm (when measured 100 km from the epicenter) rounded to the nearest tenth?

• 0.4

• 2.2

• 2.4

• 5.8

An extra-large hot chocolate is poured into a mug. The temperature, in degrees Celsius, of the hot chocolate minutes after it has been poured, can be modeled by the following equation. Approximately when will the hot chocolate be 84 degrees?

• 2 minutes

• 3 minutes

• 5 minutes

• 36 minutes

Alice would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. She was able to make a down payment of $7,400. After how many years will she have paid $15,683.28?

• 2 years

• 4 years

• 8 years

• 16 years