Which of the following graphs of exponential functions corresponds to a geometric sequence with a 1st term of 6 and a ratio of 1/2?

I'm honestly so confused on this. :(

the terms of the sequence are

6 3 1.5 .75 ,...
So, the graph comes down from the upper left, passes through (0,6) and tails off to the right with horizontal asymptote y = 12

I assume one of the displayed graphs looks like that.

If it's not clear how I came up with those numbers, spend a little time reviewing geometric series.

sorry. the asymptote is y=0

suck it perros

To determine which of the given graphs corresponds to a geometric sequence with a first term of 6 and a ratio of 1/2, we need to understand the behavior of a geometric sequence and how it relates to exponential functions.

A geometric sequence is a sequence of numbers in which each term is found by multiplying the previous term by a constant ratio. The general form of a geometric sequence is: a, ar, ar^2, ar^3, ...

In this case, the first term (a) is 6, and the ratio (r) is 1/2. So, the sequence would be: 6, (1/2)(6), (1/2)^2(6), (1/2)^3(6), ...

We can convert this sequence into exponential form, which has the general form: y = ab^x, where a is the initial value and b is the base with exponent x.

Let's evaluate the given options using this information:

- Option A: This graph shows exponential growth, where the base is greater than 1. Since our ratio is 1/2 (less than 1), we can eliminate option A.
- Option B: This graph shows exponential decay, where the base is between 0 and 1. Since our ratio is 1/2, we expect the value to decrease over time rather than increase. Therefore, we can eliminate option B.
- Option C: This graph shows exponential growth, but the base appears to be greater than 1. Therefore, we can eliminate option C.
- Option D: This graph shows exponential decay, where the base is between 0 and 1, and has the same behavior as a geometric sequence with a ratio of 1/2.

Based on this analysis, the graph that corresponds to a geometric sequence with a first term of 6 and a ratio of 1/2 is option D.

Understanding the behavior of a geometric sequence and recognizing exponential growth or decay patterns can help you determine the correct answer in these types of questions.