Logarithmic Conversions and Exponential Growth Challenges

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours? Use the exponential growth formula and convert to logarithmic form to find the time.

• 6000

• 10000

• 4000

• 8000

Tags

CCSS.HSF.LE.A.4

The pH level of a solution is measured on a logarithmic scale. If a solution has a pH of 4, how many times more acidic is it compared to a solution with a pH of 7? Apply properties of logarithms to solve this problem.

• 1000 times more acidic

• 100 times more acidic

• 10000 times more acidic

• 10 times more acidic

A car's value decreases exponentially over time. If a car is worth $20,000 today and loses 15% of its value each year, what will its value be in 5 years? Use the exponential decay formula and convert to logarithmic form to find the answer.

• $8,874.00

• $15,000.00

• $10,500.00

• $12,000.00

The half-life of a radioactive substance is 10 years. If you start with 80 grams, how much will remain after 30 years? Use the exponential decay model and apply logarithmic properties to determine the remaining amount.

• 40 grams

• 5 grams

• 20 grams

• 10 grams

Tags

CCSS.HSF.LE.A.4

A certain investment grows at a rate of 8% per year. If you invest $1,000, how long will it take for your investment to double? Use the formula for exponential growth and convert to logarithmic form to find the time required.

• Approximately 9 years

• Approximately 12 years

• Approximately 5 years

• Approximately 15 years

Tags

CCSS.HSF.LE.A.4

The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake measures 6.0 on the Richter scale, how many times more powerful is it than one that measures 4.0? Use properties of logarithms to calculate the difference in power.

• 50

• 100

• 10

• 200

A tree grows exponentially, increasing its height by 25% each year. If the tree is currently 2 meters tall, how tall will it be after 4 years? Use the exponential growth formula and convert to logarithmic form to find the height after 4 years.

• 3.00 meters

• 5.50 meters

• 4.88 meters

• 6.25 meters

The formula for the amount of a substance remaining after time t is A = A0 * e^(-kt). If A0 is 100 grams, k is 0.1, and t is 20, how much of the substance remains? Use logarithmic properties to solve for A.

• 25 grams

• 5 grams

• 13.53 grams

• 50 grams

Tags

CCSS.HSF.LE.A.4

A sound's intensity level is measured in decibels (dB), which is a logarithmic scale. If a sound is measured at 90 dB, how many times more intense is it than a sound at 80 dB? Apply properties of logarithms to find the intensity difference.

• 20 times more intense

• 2 times more intense

• 10 times more intense

• 5 times more intense

A bank offers a savings account with a 5% annual interest rate compounded annually. If you deposit $500, how long will it take for your investment to grow to $1,000? Use the exponential growth formula and convert to logarithmic form to determine the time needed.

• Approximately 14.21 years

• 20 years

• 5 years

• 10 years