Exponential Growth and Decay Concepts

This video tutorial from Howard Community College explains how to write exponential growth and decay functions. It provides examples using a bacteria colony for growth and phosphorus-32 for decay, demonstrating the use of the general formula A(t) = A0 * e^(kt). The tutorial covers solving for the constant k using logarithms and highlights the differences between growth and decay functions.

What is the initial number of bacteria in the colony at the start of the growth process?

• 250

• 150

• 300

• 200

In the exponential growth formula A(t) = A₀e^(kt), what does A₀ represent?

• The final amount

• The time period

• The initial amount

• The growth rate

How do you solve for the growth constant k in the exponential growth formula?

• By multiplying both sides by e

• By taking the natural logarithm of both sides

• By adding 200 to both sides

• By subtracting 14 from both sides

What is the value of k for the bacterial growth problem after rounding?

• 0.0159

• 0.0459

• 0.0259

• 0.0359

What is the half-life of phosphorus-32 as mentioned in the video?

• 14.29 days

• 12.29 days

• 16.29 days

• 10.29 days

In the context of half-life, what does A(t) equal at the end of the half-life period if you start with 1?

• 0.75

• 0.5

• 1

• 0.25

What is the value of k for the decay function after rounding?

• -0.0585

• -0.0485

• -0.0385

• -0.0685

In an exponential decay function, what is the sign of the constant k?

• Negative

• Zero

• Undefined

• Positive

What mathematical operation is used to isolate k in the decay function?

• Division

• Subtraction

• Addition

• Multiplication

What is the general formula for both exponential growth and decay?

• A(t) = A₀ + kt

• A(t) = A₀e^(kt)

• A(t) = A₀ - kt

• A(t) = A₀e^(-kt)