Exponential Functions

Front

What is an exponential function?

Back

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

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' in an exponential function determines the rate of growth or decay. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

What is the initial value in the exponential function y = a(b^x)?

Back

The initial value is represented by 'a', which is the value of y when x = 0.

Front

How do you identify exponential growth from a function?

Back

Exponential growth occurs when the base 'b' is greater than 1 in the function y = a(b^x).

Front

How do you identify exponential decay from a function?

Back

Exponential decay occurs when the base 'b' is between 0 and 1 in the function y = a(b^x).

Front

What is the formula for calculating the amount after 't' years in exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the amount after t years, P is the initial amount, r is the growth rate, and t is the time in years.

Front

What is the formula for calculating the amount after 't' years in exponential decay?

Back

The formula is A = P(1 - r)^t, where A is the amount after t years, P is the initial amount, r is the decay rate, and t is the time in years.

Front

If a function is modeled as y = 15(1.35)^x, what does 1.35 represent?

Back

In the function y = 15(1.35)^x, 1.35 represents the growth factor, indicating a 35% increase each year.

Front

What does it mean if a graph shows exponential growth?

Back

A graph showing exponential growth will rise sharply and continuously increase as x increases, indicating that the quantity grows faster over time.

Front

What does it mean if a graph shows exponential decay?

Back

A graph showing exponential decay will fall sharply and continuously decrease as x increases, indicating that the quantity decreases faster over time.