Mastering Exponential Equations: Word Problems & Logs

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours? Use an exponential equation to solve.

• 8000

• 10000

• 4000

• 6000

A car's value decreases by 20% each year. If the car is currently worth $15,000, how much will it be worth after 5 years? Set up an exponential equation and solve using logarithms.

• 10000.00

• 7500.50

• 4915.20

• 6000.00

A bank offers an interest rate of 5% compounded annually. If you invest $1,000, how long will it take for your investment to grow to $1,500? Use logarithms to find the answer.

• 10.24 years

• 12 years

• 15.5 years

• 8 years

A certain radioactive substance has a half-life of 10 years. If you start with 80 grams, how much will remain after 30 years? Formulate an exponential equation and solve it.

• 5 grams

• 40 grams

• 10 grams

• 20 grams

The number of users on a social media platform increases exponentially. If there are currently 1,000 users and the number triples every year, how many users will there be in 4 years? Solve the exponential equation to find the answer.

• 50000

• 81000

• 40000

• 30000

A certain species of fish in a lake is known to double in population every 2 years. If the current population is 200, what will the population be in 10 years? Use an exponential equation to solve.

• 6400

• 3200

• 12800

• 4000

A tree grows at a rate of 15% per year. If the tree is currently 2 meters tall, how tall will it be in 5 years? Set up and solve the exponential equation using logarithms.

• 4.02 meters

• 3.50 meters

• 5.00 meters

• 2.30 meters

A certain investment grows according to the formula A = P(1 + r)^t. If you invest $2,000 at an interest rate of 6% per year, how long will it take for the investment to reach $3,000? Use logarithms to solve the equation.

• 7.73 years

• 8.00 years

• 10.50 years

• 5.25 years

A certain type of bacteria grows exponentially. If the initial count is 250 and it grows to 1,000 in 4 hours, what is the growth rate? Set up the exponential equation and solve for the rate using logarithms.

• 0.2154

• 0.6123

• 0.4872

• 0.3466

A smartphone's battery lasts for 2 years before it needs to be replaced. If the battery's lifespan decreases by 10% each year, how long will it take for the battery to last only 1 year? Use an exponential equation to find the answer.

• Approximately 4.2 years

• Approximately 3.5 years

• Approximately 8.1 years

• Approximately 6.58 years