Exponential Growth & Logarithmic Conversion Challenges

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

• 4000

• 10000

• 2000

• 8000

A car's value decreases by 20% each year. If the car is currently worth $15,000, what will its value be after 5 years? Use logarithms to find the time it takes for the value to drop below $5,000.

• $3,000 after 5 years; it takes 2.5 years to drop below $5,000

• $4915.20 after 5 years; it takes approximately 3.64 years for the value to drop below $5,000.

• $10,000 after 5 years

• $7,500 after 5 years; it takes 4.2 years to drop below $5,000

A bank offers an account with an interest rate of 5% compounded annually. If you deposit $1,000, how much will you have after 10 years? Convert the final amount into a logarithmic equation to find the time needed to double your investment.

• 2000.00

• 1200.50

• 1500.00

• 1628.89

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 20 years? Graph the function and analyze the decay.

• 25 grams

• 5 grams

• 50 grams

• 13.53 grams

A certain species of fish in a lake grows exponentially. If the population is currently 200 and grows at a rate of 15% per year, how many fish will there be in 5 years? Use logarithms to determine when the population will reach 1,000.

• 350 fish in 5 years; population reaches 1,000 in approximately 10 years.

• 423 fish in 5 years; population reaches 1,000 in approximately 12.9 years.

• 300 fish in 5 years; population reaches 1,000 in approximately 8 years.

• 500 fish in 5 years; population reaches 1,000 in approximately 15 years.

The pH level of a solution is measured on a logarithmic scale. If a solution has a pH of 4, what is the concentration of hydrogen ions in moles per liter? Convert the pH to an exponential form to find the concentration.

• 0.1 moles per liter

• 0.0001 moles per liter

• 0.01 moles per liter

• 0.00001 moles per liter

A certain investment grows according to the function A(t) = 2000 * (1.05)^t. How long will it take for the investment to reach $3,000? Use logarithms to solve for t and graph the function.

• Approximately 10.24 years

• Approximately 15.75 years

• Approximately 8.50 years

• Approximately 5.12 years

The number of views on a viral video can be modeled by the function V(t) = 1000 * e^(0.5t). If the video was posted 4 days ago, how many views does it have now? Graph the function and predict the views after 10 days.

• After 4 days, the video has approximately 20000 views. After 10 days, it is predicted to have approximately 300000 views.

• After 4 days, the video has approximately 5000 views. After 10 days, it is predicted to have approximately 20000 views.

• After 4 days, the video has approximately 15154 views. After 10 days, it is predicted to have approximately 148413 views.

• After 4 days, the video has approximately 10000 views. After 10 days, it is predicted to have approximately 100000 views.