24-25 T2U8 Test Review

Front

What is the definition of 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 exponent.

Front

How do you determine the value of a function at a specific point, such as f(-3) for f(x) = 2(4)^x?

Back

To determine f(-3), substitute -3 for x in the function: f(-3) = 2(4)^(-3) = 2 * (1/64) = 1/32.

Front

What distinguishes a linear function from an exponential function?

Back

A linear function has a constant rate of change and can be represented by a straight line, while an exponential function has a variable rate of change that increases or decreases exponentially.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is f(n) = a * r^(n-1), where a is the first term, r is the common ratio, and n is the term number.

Front

How do you find the 10th term of a geometric sequence given the explicit formula f(n) = 3(4)^(n-1)?

Back

To find the 10th term, substitute n = 10 into the formula: f(10) = 3(4)^(10-1) = 3(4^9) = 786432.

Front

What is the relationship between the bases and exponents in exponential expressions?

Back

In exponential expressions, the base is raised to the power of the exponent, which indicates how many times the base is multiplied by itself.

Front

What does it mean for a function to be exponential in terms of growth?

Back

An exponential function exhibits rapid growth or decay, where the rate of change increases or decreases multiplicatively rather than additively.

Front

How can you identify whether a function is linear or exponential from a table of values?

Back

A linear function will show a constant difference between consecutive values, while an exponential function will show a constant ratio between consecutive values.

Front

What is the significance of the term 'k' in the expression 10(10^x)?

Back

In the expression 10(10^x), the term '10' is a coefficient that scales the exponential function, and it can be rewritten as 10^(x+1) using the properties of exponents.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.