Exploring Exponential Growth and Decay Concepts

What does exponential growth indicate about the relationship between input (X) and output (Y)?

• There is no relationship between X and Y.

• As X increases, Y also increases.

• As X increases, Y remains constant.

• As X increases, Y decreases.

What does the 'a' in the exponential growth equation represent?

• The growth rate

• The decay factor

• The initial amount

• The variable of time

How is the growth factor 'B' in an exponential growth equation determined?

• B = growth rate / initial amount

• B = 1 - growth rate

• B = 1 + growth rate

• B = initial amount * growth rate

In the context of exponential growth, what does a growth rate of 50% translate to in the equation?

• B = 0.5

• B = 1.5

• B = 2

• B = 1

What is the primary goal when applying exponential growth equations to real-world problems?

• To find the growth rate exclusively

• To identify the decay factor

• To calculate the final amount after a certain period

• To determine the initial amount only

What distinguishes exponential decay from exponential growth?

• The initial amount is not relevant in decay

• The output increases as the input increases

• The output decreases as the input increases

• The decay factor is always greater than 1

In exponential decay, how is the decay factor 'B' calculated?

• B = 1 + decay rate

• B = decay rate - 1

• B = decay rate / initial amount

• B = 1 - decay rate

What does a decay rate of 13% imply in an exponential decay equation?

• The value decreases by 87% each year.

• The value decreases by 13% each year.

• The decay factor is 0.87.

• The decay factor is 1.13.

What is the significance of compounding monthly in the context of compound interest?

• It increases the frequency of interest application, potentially increasing the total amount.

• It has no effect on the interest.

• It changes the principal amount.

• It decreases the total amount of interest earned.

How is the half-life used in the formula for radioactive decay?

• It is added to the initial amount.

• It is the exponent in the decay equation.

• It determines the decay rate.

• It is used to calculate the remaining amount after a period.