Exploring Exponential Growth and Logarithmic Applications

A certain investment grows exponentially at a rate of 5% per year. If you invest $1000, how long will it take for your investment to reach $2000? Use logarithms to solve for the time.

• Approximately 20 years

• Approximately 14.2 years

• Approximately 5 years

• Approximately 10 years

The value of a car 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 logarithms to find the time it takes to reach a value of $10,000.

• $15,000 in 5 years and 6.2 years to reach $10,000

• $10,000 in 5 years and 7.5 years to reach $10,000

• $12,000 in 5 years and 4.5 years to reach $10,000

• The value of the car in 5 years is approximately $8,874.00, and it takes about 5.74 years to reach a value of $10,000.

A certain species of fish in a lake is known to grow exponentially. If the population is currently 200 and grows at a rate of 10% per month, how long will it take for the population to reach 500? Use logarithms to determine the time.

• 9.1 months

• 20 months

• 15 months

• 5 months

A bank account earns interest compounded continuously at a rate of 4%. If you want to have $5000 in the account, how much do you need to deposit today? Use logarithms to find the initial deposit amount.

• 4803.19

• 4900.75

• 5200.50

• 4500.00

A radioactive substance decays exponentially. If the half-life of the substance is 10 years, how much of a 100g sample will remain after 30 years? Use logarithms to calculate the remaining amount.

• 75g

• 50g

• 12.5g

• 25g

A tree grows exponentially at a rate of 20% per year. If the tree is currently 3 meters tall, how tall will it be in 4 years? Use logarithms to find the height after 4 years.

• 4.5 meters

• 5.0 meters

• 6.22 meters

• 8.0 meters

The population of a city is currently 1 million and is expected to grow at a rate of 3% per year. How long will it take for the population to reach 1.5 million? Use logarithms to solve for the time.

• Approximately 14.9 years

• Approximately 10.5 years

• Approximately 20.2 years

• Approximately 12.3 years

A certain type of investment grows exponentially. If you invest $500 and it grows to $1500 in 5 years, what is the annual growth rate? Use logarithms to find the growth rate.

• 10.25%

• 30.00%

• 15.00%

• 24.57%

A certain species of plant doubles in size every month. If the plant is currently 2 cm tall, how tall will it be in 6 months? Use logarithms to determine the height after 6 months.

• 128 cm

• 32 cm

• 256 cm

• 64 cm