Mastering Exponential & Logarithmic Equations: Grade 11 Quiz

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours?

• 2000

• 8000

• 10000

• 4000

The value of a car decreases exponentially. If a car is worth $20,000 and loses 15% of its value each year, what will its value be after 3 years?

• $12,282.50

• $15,000

• $18,000

• $10,000

A certain investment grows exponentially. If you invest $1,000 at an annual interest rate of 5%, how much will you have after 10 years?

• 1500.00

• 1628.89

• 1200.50

• 2000.00

The half-life of a radioactive substance is 5 years. If you start with 80 grams, how much will remain after 15 years?

• 5 grams

• 20 grams

• 10 grams

• 40 grams

A sound level is measured in decibels (dB) and is given by the formula L = 10 log(I/I0), where I is the intensity of the sound and I0 is a reference intensity. If a sound has an intensity of 1000 times the reference intensity, what is its sound level in decibels?

• 10 dB

• 50 dB

• 100 dB

• 30 dB

A bank offers a savings account with an interest rate of 4% compounded annually. How long will it take for an investment of $2,000 to grow to $3,000?

• Approximately 20 years

• Approximately 15 years

• Approximately 5 years

• Approximately 11.18 years

The population of a city is modeled by the equation P(t) = P0e^(kt), where P0 is the initial population, k is the growth rate, and t is time in years. If the population is currently 50,000 and is expected to grow to 70,000 in 5 years, what is the growth rate k?

• 0.0733

• 0.045

• 0.1

• 0.05

If the pH level of a solution is given by the formula pH = -log[H+], where [H+] is the concentration of hydrogen ions, what is the concentration of hydrogen ions in a solution with a pH of 3?

• 1 M

• 0.1 M

• 0.001 M

• 0.01 M

A certain species of fish is introduced to a lake and its population grows according to the model P(t) = 200e^(0.1t). How long will it take for the population to reach 1,000 fish?

• 10.25

• 16.09

• 30.75

• 25.50

The formula for the decay of a substance is given by N(t) = N0e^(-kt). If a substance has a half-life of 10 years, what is the value of k?

• 0.05

• 0.2

• 0.1

• 0.0693