Exponential Growth & Logarithmic Equations: Grade 10 Quiz

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

• 4000

• 8000

• 10000

• 2000

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?

• 10440.13

• 12000.50

• 8500.75

• 15000.00

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?

• 2000.00

• 1500.00

• 1628.89

• 1200.50

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

• 40 grams

• 20 grams

• 5 grams

A certain species of fish in a lake is modeled by the function P(t) = 200e^(0.3t), where P is the population and t is time in years. What is the population after 5 years?

• 500

• 1200

• 750

• 896

A bank offers an account that compounds interest continuously at a rate of 4%. If you deposit $2,000, how much will you have after 3 years?

• 2400.00

• 2255.00

• 2100.00

• 2005.00

The formula for the amount of a substance remaining after t years is A(t) = A_0 * (1/2)^(t/h), where A_0 is the initial amount and h is the half-life. If the half-life is 10 years and you start with 160 grams, how much will remain after 20 years?

• 20 grams

• 80 grams

• 40 grams

• 100 grams

A tree grows according to the model h(t) = 5(2^t), where h is the height in meters and t is the time in years. What is the height of the tree after 6 years?

• 250 meters

• 150 meters

• 320 meters

• 400 meters

The population of a city is modeled by the equation P(t) = 50,000e^(0.02t). How long will it take for the population to reach 100,000?

• 50 years

• 15 years

• 34.66 years

• 20 years

If the logarithm of a number x to the base 10 is 3, what is the value of x?

• 10000

• 1000

• 10

• 100