Exponential Growth & Logarithmic Equations Challenge

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

• 8000

• 4000

• 10000

• 2000

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

• 12000.50

• 15000.00

• 8500.75

• 10440.13

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

• 5 grams

• 20 grams

• 40 grams

• 10 grams

A sound level is measured in decibels (dB) and is given by the formula L = 10 log(I/I0), where I is the intensity of the sound and I0 is a reference intensity. If a sound has an intensity of 1000 times the reference intensity, what is its sound level in decibels?

• 10 dB

• 30 dB

• 50 dB

• 100 dB

A certain type of bacteria grows according to the equation P(t) = P0e^(kt). If the initial population is 200 and the growth rate k is 0.03, what will the population be after 10 hours?

• 320

• 250

• 300

• 270

If the logarithm of a number is 2, what is the number?

• 50

• 100

• 1000

• 10

A bank offers a savings account with a 4% interest rate compounded annually. If you deposit $2,500, how much will you have in the account after 5 years?

• $3,500.00

• $3,041.63

• $2,500.00

• $2,000.00

The formula for the decay of a substance is N(t) = N0e^(-kt). If the initial amount is 100 grams and the decay constant k is 0.1, how much will remain after 10 hours?

• 36.79 grams

• 75 grams

• 50 grams

• 25 grams

If the equation 3^x = 81 is solved for x, what is the value of x?

• 5

• 9

• 4

• 3