Exploring Exponential Growth & Logarithmic Scales

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

• 2000

• 10000

• 4000

• 8000

The value of a car decreases by 15% each year. If the car is currently worth $20,000, what will its value be after 4 years?

• $10,440.12

• $15,000.00

• $8,500.00

• $12,000.00

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?

• 1200.50

• 2000.00

• 1500.00

• 1628.89

The pH scale is logarithmic. If a solution has a pH of 3, how many times more acidic is it compared to a solution with a pH of 6?

• 10 times more acidic

• 10000 times more acidic

• 100 times more acidic

• 1000 times more acidic

A tree grows at a rate of 10% per year. If the tree is currently 2 meters tall, what will its height be after 5 years?

• 3.22 meters

• 2.00 meters

• 4.00 meters

• 5.00 meters

The population of a city is modeled by the function P(t) = 50,000e^(0.03t), where t is the number of years since 2000. What will the population be in 2025?

• 95000

• 120000

• 80000

• 105850

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

• 40 grams

• 5 grams

• 20 grams

• 10 grams

The Richter scale measures the magnitude of earthquakes logarithmically. If an earthquake measures 6.0 on the Richter scale, how much more powerful is it than one that measures 4.0?

• 10 times more powerful

• 100 times more powerful

• 200 times more powerful

• 50 times more powerful

A bank offers a savings account with an annual interest rate of 4%, compounded annually. How much money will you have in the account after 3 years if you deposit $1,200?

• $1,349.84

• $1,500.00

• $1,200.00

• $1,100.00

The formula for exponential growth is given by A = Pe^(rt). If you have an initial amount of $500, a growth rate of 6%, and you want to find the amount after 8 years, what is A?

• 600

• 808

• 750

• 900