Exponential Growth and Decay

Front

What is the general formula for exponential decay?

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What is the general formula for exponential growth?

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

How do you determine the decay factor from a percentage decay rate?

Back

The decay factor is calculated as 1 - (decay rate). For example, if the decay rate is 30%, the decay factor is 0.7.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over equal time intervals.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over equal time intervals.

Front

If a population of bacteria decreases by 30% each year, what is the equation representing this situation?

Back

y = 5000(0.7)^t, where 5000 is the initial population and 0.7 is the decay factor.

Front

What is the decay factor for a car that depreciates at a rate of 8% per year?

Back

The decay factor is 0.92, calculated as 1 - 0.08.

Front

How do you classify the model A=1200(0.85)^6?

Back

This model represents exponential decay because the base (0.85) is less than 1.

Front

What is the initial amount in the function y = 15(1.35)^t?

Back

The initial amount is $15.

Front

If a population of fish starts at 8,000 and decreases by 6% per year, how do you calculate the population after 10 years?

Back

Use the formula y = 8000(0.94)^10 to find the population after 10 years.