Logarithmic Equations: Identify Variables & Solve Problems

A scientist is studying bacteria growth. The number of bacteria doubles every hour. If there are initially 100 bacteria, how many hours will it take for the bacteria to reach 800? Identify the variable and solve the equation using logarithms.

• 5 hours

• 4 hours

• 2 hours

• 3 hours

A car's value decreases by 20% each year. If the car is currently worth $15,000, how long will it take for the car's value to drop below $5,000? Set up the equation and solve for the time using logarithms.

• 10

• 4

• 8

• 6

A phone company sells a new model for $800. After a year, the price drops to $600. If the price decreases by a constant percentage each month, how many months will it take for the price to reach $400? Identify the variable and solve the equation.

• 24 months

• 12 months

• 30 months

• 18 months

A population of a town is 10,000 and is decreasing by 5% each year. How many years will it take for the population to fall below 5,000? Set up the equation and solve using logarithms.

• 12

• 20

• 15

• 10

A bank offers an interest rate of 3% compounded annually. If you invest $1,000, how long will it take for your investment to grow to $1,500? Identify the variable and solve the equation using logarithms.

• Approximately 5 years

• Approximately 20 years

• Approximately 12.2 years

• Approximately 8.5 years

A tree grows at a rate of 10% per year. If the tree is currently 2 meters tall, how many years will it take for the tree to reach 5 meters? Set up the equation and solve using logarithms.

• 10 years

• 5 years

• 8 years

• 12 years

A certain species of fish doubles its population every 3 years. If the current population is 200, how long will it take for the population to reach 1,600? Identify the variable and solve the equation using logarithms.

• 15 years

• 9 years

• 12 years

• 6 years

A student scores 80% on a test. If the test has 50 questions, how many questions did the student answer correctly? Set up the equation and solve for the number of correct answers using logarithms.

• 30

• 45

• 25

• 40

A recipe calls for 2 cups of sugar, and you want to make a batch that is 8 times larger. How many cups of sugar will you need? Identify the variable and solve the equation using logarithms.

• 20 cups

• 12 cups

• 16 cups

• 8 cups

A phone's battery lasts for 10 hours on a full charge. If it discharges at a rate of 15% per hour, how long will it take for the battery to drop below 50%? Set up the equation and solve using logarithms.

• 5 hours

• 6 hours

• 4 hours

• 7 hours