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.