StudyGPT Just Leveled Up – Say Hello to Knowee! 🚀
Knowee
Questions
Features
Study Tools

Select the correct answer.Which graph shows an exponential function that nears a constant value as x approaches positive infinity and has a y-inte

Question

🧐 Not the exact question you are looking for?Go ask a question

Solution

To select the correct answer for the graph displaying an exponential function that approaches a constant value as x x approaches positive infinity and has a y-intercept, we need to look for key characteristics of exponential functions.

  1. Exponential Function Behavior:

    • Exponential functions can take forms such as y=abx y = a \cdot b^x , where:
      • a a is the y-intercept (when x=0 x = 0 ).
      • b b determines the growth or decay.
    • For the function to approach a constant value as x x approaches positive infinity, we typically consider functions that have a horizontal asymptote.
  2. Horizontal Asymptote:

    • If the function approaches a constant value L L , it would resemble forms like y=L+aebx y = L + a \cdot e^{-bx} or y=L+abx y = L + a \cdot b^{-x} for certain values of a a and b b , where b>1 b > 1 indicates decay.
  3. Y-Intercept:

    • The y-intercept will be the value of the function when x=0 x = 0 .

Given these points, check each graph to identify:

  • Which graph moves closer to a horizontal line (indicating that it approaches a constant value).
  • Identify the y-intercept from the graph.

Final Answer

The correct choice will be the graph that shows an exponential decay approach towards a horizontal line as x x increases, with a clear y-intercept value at x=0 x = 0 .

This problem has been solved

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.