APPC Unit 2A Review

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 variable. It describes growth or decay processes.

Front

How do you write the function for a given table of values?

Back

To write the function for a table of values, identify the pattern in the data points, determine if it follows a linear, quadratic, or exponential trend, and then derive the function accordingly.

Front

What is the half-life in the context of exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value. In exponential decay, it is a constant rate at which the quantity decreases.

Front

Back

Front

What does the limit of a function as x approaches infinity represent?

Back

The limit of a function as x approaches infinity represents the value that the function approaches as the input grows larger and larger.

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' is the initial value and 'b' is the growth factor (b > 1).

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 'a' is the initial value and '0 < b < 1' is the decay factor.

Front

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

Back

The y-intercept of an exponential function f(x) = a * b^x is found by evaluating f(0), which equals 'a'.

Front

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

Back

The base of an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you find the number of bacteria after a certain time given a half-life?

Back

To find the number of bacteria after a certain time, use the formula: N(t) = N0 * (1/2)^(t/T), where N0 is the initial amount, t is the elapsed time, and T is the half-life.