Unit 6 Test Review

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

In the equation S_n = a(b)^n, what do 'a' and 'b' represent?

Back

'a' represents the initial value or the first term of the sequence, and 'b' represents the common ratio or the factor by which the sequence grows.

Front

How do you determine if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if each x-value is paired with exactly one y-value. If an x-value repeats with different y-values, it is not a function.

Front

What is the value of 't' in the equation 960 = 30(2)^t when solving for the number of days it takes for bacteria to grow?

Back

To solve for 't', you would rearrange the equation to find t = log2(960/30). This simplifies to t = log2(32) = 5.

Front

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

Back

The base in an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the first term of the sequence 2, 4, 8, 16, ...?

Back

The first term of the sequence is 2.

Front

How can you express the sequence 4, 8, 16, 32, 64 in exponential form?

Back

The sequence can be expressed as S_n = 2(2)^n, where n starts from 0.

Front

What does it mean for a function to be exponential?

Back

A function is considered exponential if it can be expressed in the form y = a(b)^x, where the variable x is in the exponent.

Front

What is the solution to the equation 4^(2x-5) = 64?

Back

The solution is x = 4.

Front

What is the relationship between the terms in the sequence 2, 4, 8, 16, ...?

Back

Each term in the sequence is obtained by multiplying the previous term by 2.