Sally graphs the geometric sequence an = 2(3)n - 1 on a coordinate plane where she plots an on the y-axis and n on the x-axis. This graph is the same as the graph of which type of function?
A) cubic
B) linear <my answer
C) quadratic
D) exponential
I have a suspicion that your equation looked something like
an = 2(3^n) - 1
or else , why wouldn't they have written it as
an = 6n - 1 , which would indeed be linear,
If it is as I suspected, it would be exponential.
To determine the type of function represented by the graph of the geometric sequence, let's first understand what a geometric sequence is.
A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a constant value called the common ratio. In the given sequence, the term an = 2(3)n - 1, the common ratio is 3.
Now, let's look at the equation of the given sequence, an = 2(3)n - 1. We can rewrite it using exponentiation to make it easier to analyze:
an = 2 * (3)n * 1
By rearranging the terms, we get:
an = (2 * 3 * 1)n
Now, let's compare this equation to the general form of different types of functions:
A) Cubic function: y = ax^3
B) Linear function: y = mx + b
C) Quadratic function: y = ax^2 + bx + c
D) Exponential function: y = ab^x
Comparing the given equation with each type of function:
A) Cubic function: The given equation does not have a cubic form since it does not involve cubing the variable "n".
B) Linear function: The given equation does not have a linear form since it involves exponentiation and not just a simple variable or constant multiplication.
C) Quadratic function: The given equation does not have a quadratic form since it does not involve squaring the variable "n".
D) Exponential function: The given equation has the same form as an exponential function, y = ab^x. In this case, the base (b) is 3 and the coefficient (a) is 2 * 1 = 2.
Therefore, the correct answer is D) exponential. The graph of the geometric sequence an = 2(3)n - 1 is the same as the graph of an exponential function.
Correct answer: D) exponential
Explanation:
A geometric sequence is a sequence of numbers in which each term is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
In this case, the formula for the nth term of the geometric sequence is given by an = 2(3)n - 1.
When we plot the values of an on the y-axis and n on the x-axis, we will see that the values of an are increasing exponentially.
Exponential functions have the form y = ab^x, where a and b are constants. In this case, the constant a is 2 and the base b is 3.
Therefore, the graph of the given sequence an = 2(3)n - 1 is the same as the graph of an exponential function.