Exponential Equations and Logarithmic Conversions Quiz

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

• 4000

• 6000

• 8000

• 10000

The value of a car decreases exponentially. If a car is worth $20,000 and loses 15% of its value each year, what will its value be after 3 years?

• $12,282.50

• $18,000

• $10,000

• $15,000

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?

• 10 grams

• 5 grams

• 40 grams

• 20 grams

A tree grows at an exponential rate, reaching a height of 10 meters in 5 years. If it continues to grow at the same rate, how tall will it be in 10 years?

• 20 meters

• 30 meters

• 25 meters

• 15 meters

A certain species of fish in a lake triples in population every year. If there are currently 200 fish, how many will there be in 4 years?

• 4000

• 6400

• 800

• 16200

The formula for the amount of money A after t years with principal P and interest rate r is A = Pe^(rt). If you invest $1,500 at an annual interest rate of 4% for 5 years, how much will you have?

• 2000.00

• 1750.50

• 1832.10

• 1500.00

If the equation 3^(2x) = 81 is true, what is the value of x?

• 2

• 4

• 3

• 1

Convert the logarithmic equation log_2(32) = x into exponential form and find the value of x.

• 8

• 6

• 5

• 4