Graphing Exponential Functions

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 a positive real number, and 'x' is the exponent.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in f(x) = a * b^x is greater than 1, leading to an increase in value. Exponential decay occurs when 'b' is between 0 and 1, leading to a decrease in value.

Front

How do you identify exponential growth from a function?

Back

If the base 'b' in the function f(x) = a * b^x is greater than 1, the function represents exponential growth.

Front

How do you identify exponential decay from a function?

Back

If the base 'b' in the function f(x) = a * b^x is between 0 and 1, the function represents exponential decay.

Front

What is the range of an exponential function f(x) = a * b^x + k?

Back

The range is (k, ∞) if a > 0 and (−∞, k) if a < 0, where 'k' is a vertical shift.

Front

What is the anchor point of an exponential function?

Back

The anchor point is the point where the function intersects the y-axis, typically at (0, a + k) for f(x) = a * b^x + k.

Front

What happens to the value of a penny doubled every day for 30 days?

Back

It grows exponentially, resulting in over $5 million by the end of 30 days.

Front

What is the formula for calculating the value of an exponential function?

Back

The formula is f(x) = a * b^x, where 'a' is the initial value, 'b' is the growth/decay factor, and 'x' is the time or number of periods.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives f(0) = a * b^0 = a.

Front

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

Back

The base 'b' determines the rate of growth or decay; a larger 'b' indicates faster growth, while a smaller 'b' (but greater than 0) indicates slower decay.