Exponential Functions Study Guide #1

Front

What is the y-intercept in the function f(x)=13(.27)^x?

Back

The y-intercept is 13.

Front

Does the equation y = 500(.30)^x + 7 model growth or decay?

Back

It models decay by 70%.

Front

What is the initial value in an exponential function?

Back

The initial value is the starting value when the input is zero.

Front

What is the horizontal asymptote of a function?

Back

The horizontal asymptote is the line that the graph approaches as x approaches infinity, in this case, y=2.

Front

How is the growth rate determined for an exponential function?

Back

The growth rate is determined by the value of the base.

Front

What does an exponential function generally look like?

Back

An exponential function has the form f(x) = a(b)^x, where a is the initial value and b is the base.

Front

What is the difference between growth and decay in exponential functions?

Back

Growth occurs when the base (b) is greater than 1, while decay occurs when the base (b) is between 0 and 1.

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

What does the base of an exponential function represent?

Back

The base represents the growth or decay factor per time unit.