A computer’s resale price, in dollars, years after it was purchased, is modeled by the function
According to the model, what is the computer’s resale price years after it was purchased?
An exponential decay model repeatedly multiplies a value by a factor below . When the question gives a function and asks for the price at a known year, put that year into the function and evaluate it in Desmos. The exponent counts intervals, not individual years, so read its denominator before applying the factor.
Hints
- Hint 1
The number of years is the function’s input, and the price is its output. To find the price after years, what do you get when you replace with ?
- Hint 2
An exponent tells you how many times to apply the factor. Here, dividing the years by counts two-year intervals. How many of those intervals fit into years?
Step-by-step
Evaluate the given model
Step 1Turn four years into a function value
The problem uses for years after purchase, so four years means . Function notation means the price at that input. Replace with :
- Step 2
Count the two-year intervals
The exponent counts applications of the factor . Because , four years contains two two-year intervals. Simplify the exponent:
Applying four times would ignore the division by .
- Step 3
Enter the model in Desmos
Type the full rule on one line. Desmos recognizes as a function, so you can use its name on the next line without retyping the rule.
- Step 4
Read the resale price
Type below the rule. Desmos shows , so the model gives a resale price of $960 after years. Choice B.