Logarithmic and Exponential Growth: Real-World Problems

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

• 16000

• 4000

• 1000

• 8000

The pH level of a solution is measured on a logarithmic scale. If a solution has a pH of 4, what is the hydrogen ion concentration in moles per liter?

• 0.1 moles per liter

• 0.01 moles per liter

• 0.0001 moles per liter

• 1 mole per liter

A car's value decreases exponentially over time. If a car is worth $20,000 and loses 15% of its value each year, what will its value be after 5 years?

• $12,000.00

• $8,874.77

• $10,500.50

• $15,000.00

The half-life of a radioactive substance is 10 years. If you start with 80 grams, how much will remain after 30 years?

• 40 grams

• 10 grams

• 5 grams

• 20 grams

A certain investment grows exponentially. If you invest $1,000 at an annual interest rate of 5%, how much will you have after 10 years?

• 1200.50

• 2000.00

• 1628.89

• 1500.00

The formula for the decay of a substance is given by A(t) = A0 * e^(-kt). If A0 = 100 grams, k = 0.1, and t = 20, how much of the substance remains?

• 50 grams

• 25 grams

• 5 grams

• 13.53 grams

If log_b(64) = 2, what is the value of b?

• 4

• 16

• 8

• 10

A sound intensity level is measured in decibels using the formula L = 10 log(I/I0). If the intensity I is 100 times I0, what is the sound level in decibels?

• 20 decibels

• 30 decibels

• 50 decibels

• 10 decibels

The number of users of a social media platform grows according to the model N(t) = N0 * e^(rt). If N0 = 1,000 users and r = 0.05, how many users will there be after 3 years?

• 1000

• 1162

• 1300

• 1500

If the equation 2^x = 32 is solved for x, what is the value of x?

• 5

• 6

• 8

• 4