U14 Homework 7 Logarithmic Application

You are offered a job that pays a different amount each day. The first day, you are paid 1¢. The second day you are paid 2¢. The third day you are paid 4¢. Each day, your pay continues to double. Write an equation that would describe the amount, in cents, you would be paid on any particular day.

• a(n) = n × 2

The pH of a substance is the concentration of hydrogen ions, [H+], measured in moles of hydrogen per liter of substance. It is given by the formula pH = log (1/[H+]). Find the amount of hydrogen in a liter of acid rain that has a pH of 4.2.

The Thomas family includes several generations of farmers. They have an opportunity to buy 50 acres adjacent to their farm for $800 per acre. In the past, the price of farmland has gone up 3% a year. If this continues, how long will it be before the land is worth $1,000 per acre?

• approximately 5.324 years

• approximately 6.7 years

• approximately 7.549 years

• approximately 10 years

Suppose that the population of one endangered species decreases at a rate of 6% per year. In one habitat, the current population of the species is 278. How long will it take for the population to drop below 45? (to the nearest year)

• 19 years

• 29 years

• 30 years

• 35 years

The 1991 population of Cairo, Egypt, was 10,099,000. This population is expected to grow at a rate of approximately 2.2% per year. At this rate of increase, in what year will the population exceed 15 million?

• 2005

• 2010

• 2009

• 2023

The intensity level of sound, β, measured in decibels, is given by the equation β = 10 log (I/I₀), where I is the sound intensity and I₀ is the reference intensity. If I₀ = 10⁻¹² watts per square meter, what is the decibel intensity level of a sound measuring 5 watts per square meter?

• 130 dB

• 127 dB

• 151 dB

• 140 dB

The loudest sustained snoring on record measures 85 decibels. The town in which the snorer lived had a noise ordinance setting the maximum traffic noise to 80 decibels. By how many times did the intensity of the snoring compare to the maximum intensity of traffic noise? (Use the equation β = 10 log (I/I₀))

• 2 times

• 3.16 times

• 5 times

• 10 times

Suppose that $250 is deposited into an account that pays 4.5% compounded quarterly. How long until you have tripled your investment?

• 24.55 years

• 20 years

• 25 years

• 22.604 years

A veterinarian has instructed Colby to give his 75-pound dog one 325 mg aspirin tablet for arthritis. The aspirin has a half-life of 10 minutes. How much time has passed before the amount of aspirin, A, drops below 50mg?

• 30 minutes

• 27 minutes

• 40 minutes

• 19 minutes

Aiden has $7750 in an account that earns 4% interest compounded continuously. After a certain period of time, he checks his account and finds that there is $9,465.87 in the account. How long was Aiden’s money invested? (Round to the nearest whole year)

• 4 years

• 5 years

• 6 years

• 7 years