Writing Exponential Functions (Word Problems)

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

Front

How do you write an exponential decay function?

Back

An exponential decay function can be written as f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

If a quantity decreases by 30% each year, what is the decay factor?

Back

The decay factor is 0.7, which means you multiply the initial amount by 0.7 each year.

Front

How do you model the depreciation of a car's value?

Back

To model depreciation, use the formula V(t) = a(1 - r)^t, where 'a' is the initial value, 'r' is the depreciation rate, and 't' is time in years.

Front

What does the y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value of the function when x = 0.

Front

How do you find the number of cells after a certain time if they triple every hour?

Back

Use the function f(h) = a(3)^h, where 'a' is the initial number of cells and 'h' is the number of hours.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth increases over time, while exponential decay decreases over time.

Front

How can you identify an increasing exponential function?

Back

An increasing exponential function has a base greater than 1, which causes the function to rise as x increases.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b)^x, where 'a' is a constant and 'b' is the base.