70.6k views
4 votes
For the x-values 1, 2, 3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of function is it?   A. Exponential growth   B. Decreasing linear   C. Increasing linear   D. Exponential decay

User Oceanclub
by
7.4k points

2 Answers

2 votes

Final answer:

The function described, where y-values form an increasing geometric sequence as x-values increase, is characterized as Exponential growth. This is consistent with an exponential curve where the rate of growth is proportional to the current value, which aligns with the behavior of a geometric sequence.

Step-by-step explanation:

For the given scenario where the y-values of a function form a geometric sequence that increases for the x-values 1, 2, 3, and so on, the type of function is described as Exponential growth. This is because in a geometric sequence each term after the first is found by multiplying the previous term by a constant called the common ratio, which is analogous to the exponential function where the growth rate of the value is proportional to its current value. The more the x-value increases, the higher and faster the y-value grows, following the pattern of an exponential growth curve.

Answer A. Exponential growth fits the description as it involves an increasing geometric sequence. Answer B. Decreasing linear refers to a linear function that decreases with each increment in x, which does not describe the function in question. Similarly, Answer C. Increasing linear describes a function that increases at a constant rate, not geometrically. Answer D. Exponential decay would imply the y-values decrease as x increases, which is also not the case described.

User Peter Kruithof
by
8.2k points
3 votes

Answer:

Option A: Exponential growth

Step-by-step explanation:

If for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.

Option B is incorrect because because y is not decreasing

Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.

User Adam Adamski
by
8.7k points