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 2 years?

• $18,000

• $14,450

• $12,000

• $16,500

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

• 40 grams

• 20 grams

• 5 grams

• 10 grams

You invest $1,000 in a savings account that earns 5% interest compounded annually. How much money will you have after 3 years?

• 1100.00

• 1000.00

• 1157.63

• 1200.00

The formula for the amount of a substance remaining after time t is A = A0 * e^(kt). If A0 = 100 grams, k = -0.1, and t = 10, what is A?

• 36.79 grams

• 10 grams

• 25 grams

• 50 grams

If the logarithm of a number x to the base 10 is 2, what is the value of x?

• 1000

• 1

• 10

• 100

A tree grows exponentially, increasing its height by 25% each year. If the tree is currently 4 meters tall, how tall will it be after 4 years?

• 8.00 meters

• 6.00 meters

• 9.77 meters

• 12.50 meters

The population of a city can be modeled by the equation P(t) = 50,000 * e^(0.03t). What will the population be after 5 years?

• 55000

• 62000

• 60000

• 58090

If log2(x) = 5, what is the value of x?

• 8

• 64

• 32

• 16

A certain investment grows according to the formula A = P(1 + r/n)^(nt). If you invest $2,000 at an annual interest rate of 6% compounded quarterly, how much will you have after 5 years?

• 2693.71

• 3000.50

• 2800.25

• 2500.00