Exponential Growth & Logarithmic Skills Challenge

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 4 years?

• $8,000.75

• $10,440.13

• $12,500.50

• $15,000.00

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

• 40 grams

• 20 grams

The formula for the amount of money A in an account after t years with principal P and interest rate r compounded continuously is A = Pe^(rt). If you invest $1,000 at an annual interest rate of 5%, how much will you have after 10 years?

• 2000.00

• 1500.00

• 1200.50

• 1648.72

If 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

• 82435

• 90000

• 75000

Using the properties of logarithms, simplify log_2(32) + log_2(4). What is the result?

• 10

• 3

• 5

• 7

A certain investment grows according to the model A(t) = 2000(1.07)^t. How long will it take for the investment to reach $4,000?

• 10.24 years

• 8.5 years

• 15 years

• 5 years

If the pH level of a solution is given by the formula pH = -log[H+], what is the pH of a solution with a hydrogen ion concentration of 0.001 M?

• 1

• 7

• 3

• 10

A tree grows according to the model h(t) = 3e^(0.1t), where h is the height in meters and t is the time in years. What will be the height of the tree after 10 years?

• 8.154

• 12.789

• 10.000

• 5.432

If a certain population of fish is modeled by the equation N(t) = 1000e^(0.03t), how many fish will there be after 5 years?

• 1050

• 1300

• 900

• 1162