3-24 Exponential Functions - Review number 2

Front

What is an exponential function?

Back

A mathematical function of the form y = ab^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What characterizes exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time.

Front

What characterizes exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to rapid decreases over time.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is the domain of any exponential function?

Back

The domain of any exponential function is all real numbers.

Front

What is the range of any exponential function?

Back

The range of any exponential function is y > 0.

Front

How does the base 'b' affect the graph of an exponential function?

Back

If 0 < b < 1, the function represents exponential decay; if b > 1, it represents exponential growth.

Front

What is the value of the function y = 2^x when x = 3?

Back

y = 2^3 = 8.

Front

What happens to the graph of an exponential function as x approaches negative infinity?

Back

As x approaches negative infinity, the value of the function approaches 0.

Front

What is the y-intercept of the function y = 3(2^x)?

Back

The y-intercept is 3, which occurs when x = 0.