Final answer:
The laptop's value decreases by an exponential decay function V(t) = $750(0.80)^t, where P is $750 and r is 0.20. To find the value after a certain number of years, plug in the value of t into the decay function and calculate, potentially using a TI-83, 83+, 84, 84+ Calculator. A graph can visualize the depreciation over time.
Step-by-step explanation:
The function that represents a $750 laptop that decreases in value by 20% each year can be modeled by an exponential decay function. Let V(t) represent the value of the laptop after t years. The formula for exponential decay is V(t) = P(1 - r)^t, where P is the initial value and r is the rate of decay. In this case, P = $750 and r = 0.20 (or 20%). Therefore, the function is:
V(t) = $750(1 - 0.20)^t
V(t) = $750(0.80)^t
This function allows us to find the value of the laptop after any given number of years by simply plugging in the value of t. For example, after 3 years, the value would be V(3) = $750(0.80)^3, which can be calculated using a calculator, such as the TI-83, 83+, 84, 84+ Calculator. The value after 3 years would be V(3) = $750(0.512) = $384 (rounded to the nearest dollar). If you want to visualize the depreciation over time, you can sketch a graph with the horizontal axis representing time (t) and the vertical axis representing the value of the laptop (V(t)).