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Dwayne wants to redecorate his bedroom and decides to purchase new furniture. The following graph could be used to represent the value of the new bedroom furniture, f(x), after x years. a graph of an exponential function which decreases through the points 0 comma 1000 and 2 comma 722 and 5 tenths Which of the following statements is/are true based on the graph and the context of the problem? The function is positive on its entire domain. The domain is x ≥ 0 to represent the number of years after the bedroom furniture was purchased. The y-intercept (0, 1000) represents the initial cost of the bedroom furniture.

Answer :

The correct statements regarding the exponential function

  • The function is positive on its entire domain.
  • The domain is x ≥ 0 to represent the number of years after the bedroom furniture was purchased.
  • The y-intercept (0, 1000) represents the initial cost of the bedroom furniture.

What is an exponential function?

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

  • a is the initial value.
  • b is the rate of change.

For this problem, we have that when x = 0, y = 1000, hence the y-intercept is of (0,a) = (0,1000), and:

[tex]y = 1000b^x[/tex]

When x = 2, y = 722.5, hence we use it to find b, as follows:

1000b² = 722.5

b² = 0.7225

b = sqrt(0.7225)

b = 0.85.

Hence the equation is:

[tex]y = 1000(0.85)^x[/tex]

The asymptote is at y = 0, hence the function is positive in the entire domain, and the and the domain is x ≥ 0 to represent the number of years after the bedroom furniture was purchased, as in these problems time is non-negative.

More can be learned about exponential functions at https://brainly.com/question/25537936

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