Mastering Exponential Growth and Logarithmic Equations

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

• 8000

• 10000

• 4000

• 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 3 years?

• $15,000

• $10,000

• $18,000

• $12,282.50

A certain investment grows exponentially at a rate of 5% per year. If you invest $1,000, how much will it be worth after 10 years?

• 2000.00

• 1500.50

• 1628.89

• 1200.00

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

• 20 grams

• 40 grams

• 10 grams

• 5 grams

A tree grows according to the function h(t) = 5e^(0.3t), 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?

• 120.50 meters

• 85.30 meters

• 75.20 meters

• 100.43 meters

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

• 5

• 6

• 4

• 8

A certain type of bacteria grows according to the model P(t) = 200e^(0.4t). How many bacteria will there be after 5 hours?

• 1200

• 1800

• 2000

• 1478

The formula for the amount of a substance remaining after t years is A(t) = A_0 * (1/2)^(t/h), where A_0 is the initial amount and h is the half-life. If A_0 is 100 grams and h is 4 years, how much will remain after 8 years?

• 25 grams

• 10 grams

• 50 grams

• 75 grams

Graph the function f(x) = 3^(x-2) and identify the y-intercept and the behavior as x approaches negative infinity.

• Y-intercept: (0, 1); As x -> -∞, f(x) -> 3.

• Y-intercept: (0, 3); As x -> -∞, f(x) -> -∞.

• Y-intercept: (0, 0); As x -> -∞, f(x) -> 1.

• Y-intercept: (0, 1/9); As x -> -∞, f(x) -> 0.

If log_2(x) = 5, what is the value of x?

• 32

• 8

• 64

• 16