Exploring Exponential Growth & Logarithmic Solutions

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

• 12 hours

• 6 hours

• 15 hours

• 10 hours

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

• 7 years

• 10 years

• 3 years

• 5 years

The amount of a radioactive substance decreases exponentially. If you start with 100 grams and it decays to 25 grams in 10 years, what is the half-life of the substance?

• 15 years

• 2.5 years

• 10 years

• 5 years

A bank offers an account that compounds interest annually at a rate of 5%. If you deposit $1,000, how long will it take for your investment to double? Use logarithms to find the answer.

• Approximately 14.21 years

• 12.5 years

• 20 years

• 10 years

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

• 0.600

• 0.350

• 0.466

• 0.250

A tree's height increases exponentially. If a tree is 2 meters tall now and will reach 10 meters in 8 years, what is the growth factor per year?

• 1.050000

• 1.300000

• 1.174618

• 1.100000

A certain type of bacteria grows exponentially. If the population is 1,000 and it triples every 4 hours, how long will it take to reach 10,000?

• 8 hours

• 6 hours

• 12 hours

• 10 hours

A loan of $5,000 is taken out at an interest rate of 8% compounded annually. How many years will it take for the loan to grow to $10,000? Use logarithms to solve.

• 5.00

• 7.50

• 9.01

• 10.50

A certain investment grows exponentially. If you invest $2,000 and it grows to $8,000 in 6 years, what is the annual growth rate?

• 26.24%

• 20.50%

• 32.10%

• 15.75%

A tree is planted at a height of 1 meter and grows exponentially. If it reaches 5 meters in 10 years, what is the growth rate per year?

• 0.2003

• 0.1609

• 0.1457

• 0.1205