Mastering Exponential Growth and Logarithmic Equations

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 12 hours?

• 6000

• 4000

• 8000

• 10000

The value of a car decreases by 15% each year. If the car is currently worth $20,000, what will its value be after 4 years?

• $15,000.00

• $10,440.13

• $8,500.75

• $12,000.00

A certain investment grows exponentially at a rate of 5% per year. If you invest $1,000, how much will it be worth after 10 years?

• 1200.00

• 1628.89

• 1500.50

• 2000.00

The half-life of a radioactive substance is 5 years. If you start with 80 grams, how much will remain after 15 years?

• 5 grams

• 20 grams

• 40 grams

• 10 grams

A tree grows at a rate of 10% per year. If it is currently 2 meters tall, how tall will it be in 5 years?

• 2.5 meters

• 3.22 meters

• 5.0 meters

• 4.0 meters

The population of a city is modeled by the equation P(t) = 2000e^(0.03t), where t is the time in years. What will the population be after 10 years?

• 2500

• 3000

• 2700

• 3200

If the equation 2^x = 32, what is the value of x?

• 8

• 6

• 5

• 4

A certain type of bacteria grows according to the model N(t) = 100e^(0.1t). How many bacteria will there be after 20 hours?

• 739

• 300

• 1000

• 500

If the equation log_10(x) = 3, what is the value of x?

• 10

• 1000

• 10000

• 100

A loan of $5,000 is taken out at an interest rate of 6% compounded annually. How long will it take for the loan to double in value?

• Approximately 11.90 years

• Approximately 5 years

• Approximately 20 years

• Approximately 15 years