Exponential Growth & Logarithmic Equations for 10th Grade

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours? Convert your answer to logarithmic form to find the time it takes to reach 8000 bacteria.

• 8000 bacteria after 12 hours; it takes 12 hours to reach 8000 bacteria.

• 4000 bacteria after 12 hours; it takes 6 hours to reach 8000 bacteria.

• 6000 bacteria after 12 hours; it takes 9 hours to reach 8000 bacteria.

• 10000 bacteria after 12 hours; it takes 15 hours to reach 8000 bacteria.

The pH level of a solution is measured on a logarithmic scale. If a solution has a pH of 4, what is the hydrogen ion concentration in moles per liter? Solve the logarithmic equation to find the concentration.

• 0.1 moles per liter

• 0.0001 moles per liter

• 0.00001 moles per liter

• 0.01 moles per liter

A car's value depreciates exponentially. If a car is worth $20,000 and loses 15% of its value each year, how much will it be worth after 5 years? Convert the depreciation rate to logarithmic form to analyze the value over time.

• $8,874.34

• $12,000.00

• $10,500.00

• $15,000.00

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

• 40 grams

• 20 grams

• 5 grams

• 10 grams

A bank offers an account with an interest rate of 5% compounded annually. If you deposit $1000, how much will you have after 10 years? Use exponential growth formulas and convert to logarithmic form to find the time needed to double your investment.

• $1500 after 10 years

• $2000 after 10 years

• It will take 10 years to double your investment

• After 10 years, you will have $1628.89. It will take approximately 14.21 years to double your investment.

The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake measures 6.0 on the Richter scale, how many times more intense is it than one that measures 4.0? Solve the logarithmic equation to find the intensity difference.

• 200

• 10

• 100

• 50

The formula for the amount of a substance remaining after time t is A = A0 * e^(-kt). If A0 is 100 grams and k is 0.1, how much will remain after 20 minutes? Solve the logarithmic equation to find the remaining amount.

• 100.00 grams

• 98.50 grams

• 95.00 grams

• 96.72 grams

A tree's height increases exponentially. If a tree is currently 3 meters tall and grows at a rate of 25% per year, how tall will it be in 4 years? Use logarithmic equations to analyze the growth over time.

• 4.50 meters

• 7.00 meters

• 5.86 meters

• 6.20 meters