Exponential Key Features

Front

What does the initial value represent in an exponential function?

Back

The initial value represents the starting amount before any growth or decay occurs.

Front

In the expression 12(1.015)^t, what does the number 12 signify?

Back

The number 12 signifies the initial amount of elephants in the park.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches, often representing a value that the function cannot reach.

Front

Identify the y-intercept in the function f(x)=13(0.27)^x.

Back

The y-intercept is 13, which is the initial value when x=0.

Front

What does it mean if a graph shows exponential decay?

Back

Exponential decay means that the quantity decreases rapidly at first and then slows down over time.

Front

How can you determine if a function is exhibiting growth or decay?

Back

If the base of the exponential function is greater than 1, it shows growth; if it is between 0 and 1, it shows decay.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a(b)^x, where 'a' is the initial value and 'b' is the growth/decay factor.

Front

What does the term 'growth factor' refer to in an exponential function?

Back

The growth factor is the base of the exponential function when it is greater than 1, indicating how much the quantity increases.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a larger base indicates faster growth.

Front

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

Back

To find the y-intercept, evaluate the function at x=0.