Mastering Exponentials & Logarithms: Growth & Decay Quiz

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

• 2000

• 4000

• 10000

• 8000

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 2 years?

• $12,000

• $14,450

• $18,000

• $16,500

Convert the exponential equation 2^x = 16 into logarithmic form and solve for x.

• 4

• 16

• 8

• 2

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?

• 1628.89

• 2000.00

• 1500.50

• 1200.00

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

• 20 grams

• 40 grams

Convert the logarithmic equation log_3(81) = x into exponential form and find the value of x.

• 6

• 8

• 2

• 4

A tree grows at an exponential rate, increasing its height by 20% each year. If the tree is currently 2 meters tall, how tall will it be after 3 years?

• 2.4 meters

• 4.0 meters

• 5.2 meters

• 3.456 meters

The formula for the amount of a substance remaining after time t is A = A_0 * e^(-kt). If A_0 is 100 grams, k is 0.1, and t is 10, how much substance remains?

• 25 grams

• 36.79 grams

• 75 grams

• 50 grams

Convert the equation 5^x = 25 into logarithmic form and determine the value of x.

• 2

• 4

• 1

• 3

A certain type of bacteria grows according to the model P(t) = 200e^(0.3t). How many bacteria will there be after 4 hours?

• 500

• 800

• 664

• 1000