Exploring Exponential Growth & Logarithmic Decay Problems

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

• 6000

• 10000

• 4000

• 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 4 years?

• 12000.50

• 10440.13

• 15000.00

• 8500.75

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

• 10 grams

• 5 grams

• 20 grams

• 40 grams

The pH level of a solution is measured on a logarithmic scale. If a solution has a pH of 3, how many times more acidic is it than a solution with a pH of 6?

• 10000 times more acidic

• 1000 times more acidic

• 10 times more acidic

• 100 times more acidic

A bank offers an account that compounds interest annually at a rate of 5%. If you deposit $1,000, how much will you have in the account after 10 years?

• 1628.89

• 1200.50

• 2000.00

• 1500.00

The population of a city is modeled by the function P(t) = 50,000e^(0.02t), where t is the number of years since 2000. What will the population be in 2025?

• 100000

• 75000

• 90000

• 82435

A certain investment grows according to the formula A = P(1 + r)^t. If you invest $2,000 at an interest rate of 4% for 5 years, how much will you have at the end?

• 2500.00

• 2300.50

• 2433.31

• 2400.75

The intensity of an earthquake is measured on a logarithmic scale. If an earthquake has a magnitude of 6.0, how many times more intense is it than one with a magnitude of 4.0?

• 50

• 10

• 200

• 100

A tree grows according to the model h(t) = 3(2^t), where h is the height in meters and t is the time in years. What will be the height of the tree after 5 years?

• 48 meters

• 96 meters

• 120 meters

• 75 meters

The formula for the decay of a substance is N(t) = N0e^(-kt). If the initial amount is 100 grams and k = 0.1, how much will remain after 10 hours?

• 36.79 grams

• 25 grams

• 50 grams

• 75 grams