Exponential Growth & Logarithmic Decay: A Challenge

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

• 8000

• 4000

• 10000

• 6000

The half-life of a certain radioactive substance is 5 years. If you start with 80 grams, how much will remain after 15 years? Use a logarithmic equation to find your answer.

• 10 grams

• 40 grams

• 20 grams

• 5 grams

A car's value decreases exponentially over time. If a car is worth $20,000 today and loses 15% of its value each year, what will its value be in 5 years? Set up and solve the exponential equation.

• $12,000.00

• $8,874.04

• $10,500.00

• $15,000.00

A bank offers an account that compounds interest annually at a rate of 4%. If you deposit $1,000, how much will you have after 10 years? Use the formula for compound interest to solve.

• 1200.00

• 1600.00

• 1350.50

• 1480.24

The formula for the amount of a substance remaining after t years is A = A0 * e^(-kt). If A0 = 100 grams and k = 0.1, how much will remain after 10 years? Solve the equation using logarithms.

• 75 grams

• 36.79 grams

• 25 grams

• 50 grams

A certain investment grows according to the model A(t) = 500(1.07)^t. How long will it take for the investment to reach $1,000? Set up and solve the exponential equation.

• 10.24 years

• 15 years

• 8.5 years

• 5 years

The pH level of a solution is measured on a logarithmic scale. If a solution has a pH of 3, what is the concentration of hydrogen ions in moles per liter? Use the formula pH = -log[H+].

• 0.001 moles per liter

• 0.1 moles per liter

• 0.0001 moles per liter

• 0.01 moles per liter

A tree grows according to the model h(t) = 2(1.5)^t, where h is the height in meters and t is the time in years. What will be the height of the tree after 4 years? Solve the exponential equation.

• 10.125 meters

• 8.5 meters

• 15 meters

• 12.75 meters

The number of users of a new app is modeled by the equation N(t) = 200(1.2)^t, where t is the time in months. How many users will there be after 6 months? Solve the equation to find the answer.

• 450

• 750

• 300

• 597

A scientist measures the decay of a substance and finds that after 10 hours, 25% of the original amount remains. What is the half-life of the substance? Use logarithmic equations to determine the answer.

• 2 hours

• 5 hours

• 10 hours

• 15 hours