Question

Jay purchases a new laptop for $900 that depreciates annually. The value of his laptop per year can be modeled by the exponential function f(x) = 900(0.78)ˣ, where x is the number of years. What is the range of this exponential function in terms of the context of the problem?

Answer 1

The range of the exponential function modeling the laptop's depreciation in value, f(x) = 900(0.78)^x, is (0, $900], meaning the laptop's value will decrease over time but not fall below $0.

Step-by-step explanation:

The student's question about Jay's laptop value depreciation can be addressed by examining the given exponential function f(x) = 900(0.78)^x, where x represents the number of years. The range of this function refers to the possible values of f(x), which in the context of this problem are the possible values of the laptop's worth over time. Since the value cannot increase and it is unlikely that the laptop will have a negative value, the range of this function is (0, $900]. As time goes by, the value of the laptop will approach, but never quite reach, $0.