CFE Review Unit 8 and 9

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

How do you determine the initial value in an exponential function?

Back

The initial value in an exponential function is the value of the function when x = 0, which is represented by 'a' in the function f(x) = a * b^x.

Front

What is the decay factor in an exponential decay function?

Back

The decay factor is the base 'b' in the function f(x) = a * b^x, where 0 < b < 1. It represents the rate at which the quantity decreases.

Front

How do you find the percent rate of change in an exponential function?

Back

The percent rate of change can be found using the formula: Percent Rate of Change = (b - 1) * 100%, where 'b' is the base of the exponential function.

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base 'e', where 'e' is approximately equal to 2.71828. It is the inverse function of the exponential function.

Front

How do you solve the equation e^x = a?

Back

To solve the equation e^x = a, take the natural logarithm of both sides: x = ln(a).

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where 'a' > 0 and 'b' > 1.

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, while exponential decay occurs when 0 < b < 1.

Front

How do you write an exponential function given two points?

Back

To write an exponential function given two points (x1, y1) and (x2, y2), use the form f(x) = a * b^x and solve for 'a' and 'b' using the coordinates.

Front

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

Back

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