Exponential Growth and Decay Flashcard

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a consistent percentage over a period of time, represented by the function f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time, represented by the function f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What is the initial value in the function f(x) = 300(1.16)^x?

Back

The initial value is 300.

Front

How do you calculate the value of an asset after depreciation?

Back

Use the formula: Value = Initial Value * (1 - r)^t, where 'r' is the depreciation rate and 't' is the number of years.

Front

What is the formula for calculating the future value of an investment with exponential growth?

Back

The formula is: Future Value = Initial Amount * (1 + r)^t, where 'r' is the growth rate and 't' is the time in years.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises sharply and increases rapidly as 'x' increases.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function decreases rapidly at first and then levels off as 'x' increases.

Front

What is the formula for exponential decay?

Back

The formula is: f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

If a printer costs $35,000 and depreciates at 5% per year, what will it be worth in 8 years?

Back

The printer will be worth approximately $23,219.72.

Front

Which function represents an initial amount of $15 with a 35% increase each year?

Back

The function is y = 15(1.35)^x.