Exponential Growth & Logarithmic Equations Challenge

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

• 4000

• 6000

• 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 3 years?

• $15,000.00

• $18,000.00

• $10,000.00

• $12,282.50

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

• 20 grams

• 40 grams

• 5 grams

• 10 grams

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

• 1648.72

• 1200.50

• 2000.00

• 1500.00

If the pH level of a solution is given by the formula pH = -log[H+], what is the concentration of hydrogen ions in a solution with a pH of 3?

• 0.01 M

• 0.0001 M

• 0.001 M

• 0.1 M

A tree grows exponentially, increasing its height by 25% each year. If the tree is currently 4 meters tall, how tall will it be after 4 years?

• 12.50 meters

• 9.77 meters

• 6.00 meters

• 8.00 meters

The population of a city is modeled by the equation P(t) = 50,000e^(0.02t). What will the population be after 10 years?

• 50000

• 70000

• 80000

• 61070

If you have a logarithmic equation log(x) + log(2) = 3, what is the value of x?

• 250

• 1000

• 100

• 500

A certain investment grows according to the formula A = 500(1.07)^t. How much will the investment be worth after 5 years?

• 800.00

• 750.50

• 600.00

• 701.28

If the equation log(3x) = 2 is solved for x, what is the value of x?

• 33.33

• 50

• 10

• 20