3/26 Do now: 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 the base (a positive real number), and 'x' is the exponent.

Front

What does the variable 'P' represent in the function A = P(1 + r)^t?

Back

In the function A = P(1 + r)^t, 'P' represents the starting term or initial amount.

Front

How can you identify exponential growth?

Back

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

Front

How can you identify exponential decay?

Back

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

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the point where x = 0, which is (0, a).

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically y = 0.

Front

What is the range of the function y = a * b^x?

Back

The range of the function y = a * b^x is (0, ∞) if a > 0, and (-∞, 0) if a < 0.

Front

What does the term 'exponential growth model' refer to?

Back

An exponential growth model describes a situation where a quantity increases at a rate proportional to its current value.

Front

What does the term 'exponential decay model' refer to?

Back

An exponential decay model describes a situation where a quantity decreases at a rate proportional to its current value.

Front

How do you find the value of 'A' in the equation A = P(1 + r)^t?

Back

To find 'A', substitute the values of 'P' (initial amount), 'r' (rate of growth), and 't' (time) into the equation.