Mastering Exponential Models & Logarithmic Applications

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

• 8000

• 4000

• 2000

• 10000

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

• 10 grams

• 5 grams

• 40 grams

• 20 grams

A car's value decreases exponentially. If it is worth $20,000 now and loses 15% of its value each year, what will its value be after 4 years?

• 12000.50

• 10440.13

• 15000.00

• 8000.75

The formula for the amount of money A in an account after t years with an initial amount 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?

• $1,200.00

• $1,500.00

• $1,628.89

• $2,000.00

If the pH level of a solution is given by the formula pH = -log[H+], where [H+] is the concentration of hydrogen ions, what is the concentration of hydrogen ions in a solution with a pH of 3?

• 1 M

• 0.001 M

• 0.01 M

• 0.1 M

A certain investment grows according to the model A = Pe^(rt). If you invest $2,000 at an annual interest rate of 4% for 5 years, how much will the investment be worth?

• 3000.00

• 2000.00

• 2442.80

• 2200.50

The number of users of a new app is modeled by the function U(t) = 1000e^(0.3t), where t is the time in months. How many users will the app have after 6 months?

• 4500

• 7200

• 5000

• 6050

If the equation of a line is given by log(y) = 2x + 1, what is the value of y when x = 2?

• 10000

• 100000

• 1000

• 10

A tree grows according to the model h(t) = 5e^(0.1t), where h is the height in meters and t is the time in years. What will be the height of the tree after 10 years?

• 15.75 meters

• 13.59 meters

• 10.25 meters

• 20.00 meters

The formula for the decay of a substance is N(t) = N0e^(-kt). If a substance has a decay constant k of 0.05 and starts with 200 grams, how much will remain after 10 hours?

• 200 grams

• 150 grams

• 121.3 grams

• 80 grams