Mastering Exponential Growth & Logarithmic Applications

A population of bacteria doubles every 3 hours. If the initial population is 500, how long will it take for the population to reach 8000? Use logarithms to solve your equation.

• 15 hours

• 12 hours

• 24 hours

• 6 hours

A car's value depreciates exponentially. If a car is worth $20,000 today and loses 15% of its value each year, how many years will it take for the car's value to drop below $10,000?

• 5

• 7

• 3

• 10

A certain investment grows exponentially at a rate of 5% per year. If you invest $1,000, how long will it take for your investment to reach $1,500? Use logarithmic properties to find the answer.

• 10.24 years

• 15 years

• 12.5 years

• 8.5 years

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

• 20 grams

• 5 grams

• 40 grams

• 10 grams

A bank offers an account that compounds interest annually at a rate of 4%. If you want to have $5,000 in the account, how much do you need to deposit today? Use logarithmic equations to find the initial deposit.

• 4807.69

• 5200.50

• 5000.00

• 4500.00

A certain species of fish in a lake grows exponentially. If the population is currently 200 and grows to 1,600 in 5 years, what is the growth rate? Use logarithms to solve for the rate.

• 0.350

• 0.600

• 0.466

• 0.250

A tree's height increases exponentially. If a tree is 2 meters tall now and grows to 10 meters in 8 years, what is the annual growth rate? Use logarithmic properties to find the answer.

• 17.33%

• 12.50%

• 25.00%

• 5.25%

A certain type of mold grows at a rate of 3 times its size every 4 days. If you start with 10 grams, how long will it take to reach 1 kilogram? Use logarithms to solve the problem.

• 30 days

• 18.7 days

• 15 days

• 25 days

The number of users on a social media platform increases exponentially. If there are currently 1,000 users and the number doubles every month, how many months will it take to reach 16,000 users?

• 3 months

• 5 months

• 6 months

• 4 months

A scientist is studying a culture of cells that triples in number every 2 days. If the initial number of cells is 50, how many days will it take for the culture to exceed 10,000 cells? Use logarithmic equations to find the answer.

• 15 days

• 30 days

• 25 days

• 19 days