Exploring Exponential Growth and Logarithmic Concepts

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

• 10000

• 6000

• 8000

• 4000

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

• 20 grams

• 40 grams

• 10 grams

• 5 grams

A car's value depreciates by 20% each year. If the car was originally worth $25,000, what will its value be after 3 years?

• $12,800

• $20,000

• $10,000

• $15,000

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

• 1500.00

• 2000.00

• 1200.50

• 1628.89

A certain investment grows according to the formula A = Pe^(rt). If you invest $2,000 at an annual interest rate of 3% for 5 years, what will be the total amount?

• 2100.50

• 2400.75

• 2323.67

• 2500.00

If the population of a city is modeled by the equation P(t) = 10,000e^(0.02t), where t is the number of years since 2000, what will the population be in 2025?

• 16487

• 15000

• 20000

• 18000

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?

• 0.001 moles per liter

• 1 mole per liter

• 0.1 moles per liter

• 0.01 moles per liter

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. How tall will the tree be after 4 years?

• 40 meters

• 100 meters

• 60 meters

• 80 meters

If the sound intensity level of a sound is measured in decibels (dB) using the formula L = 10 log(I/I0), where I0 is the reference intensity, what is the intensity of a sound that measures 50 dB?

• 1e-3 W/m^2

• 1e-9 W/m^2

• 1e-5 W/m^2

• 1e-7 W/m^2

A certain species of fish in a lake is modeled by the equation N(t) = 200e^(0.1t). How many fish will there be after 10 years?

• 700

• 544

• 300

• 450