Writing Exponential Functions from 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.

Front

How do you identify the initial value in an exponential function?

Back

The initial value is represented by 'a' in the function f(x) = a(b)^x. It is the value of the function when x = 0.

Front

What does the base of an exponential function represent?

Back

The base indicates the growth or decay factor. If the base is greater than 1, the function models growth; if it is between 0 and 1, it models decay.

Front

How do you write an exponential function for growth?

Back

For growth, the function is written as f(t) = a(1 + r)^t, where 'r' is the growth rate.

Front

How do you write an exponential function for decay?

Back

For decay, the function is written as f(t) = a(1 - r)^t, where 'r' is the decay rate.

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

What is the formula for exponential decay?

Back

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

Front

How do you determine the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a(b)^x is found by evaluating f(0), which equals 'a'.

Front

What does a negative growth rate indicate in an exponential function?

Back

A negative growth rate indicates that the function is modeling decay, meaning the quantity decreases over time.

Front

How can you convert a percentage rate to a decimal for use in exponential functions?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 12% becomes 0.12.