In an exponential model, a base below multiplies the value each year rather than subtracting a fixed amount. To find the value at a stated time, evaluate the function in Desmos at that input. Then check the output’s unit: a value in thousands of dollars must be converted before you match it to a dollar amount.
Hints
- Hint 1
The input of a function is the number inside its parentheses. Here the input measures years since purchase. Which number should go inside to find the value four years later?
- Hint 2
The base is the repeated multiplier. Multiplying by keeps of the previous value each year, so don’t subtract a fixed dollar amount each year.
- Hint 3
Watch the output unit. A value measured in thousands of dollars is not yet a dollar amount. What number converts thousands of dollars to dollars?
Step-by-step
Evaluate the model, then convert units
Step 1Use four years as the input
The input counts years after purchase, so four years later means put in for :
The exponent counts four yearly multiplications, not four equal dollar losses.
- Step 2
Evaluate the resale value
Type in Desmos, then type . Desmos shows . This output is the value after four years in thousands of dollars, not the amount lost.
- Step 3
Convert the value to dollars
The output is in thousands of dollars, so multiply by to report dollars. Add in Desmos; it shows . Four years after purchase, the estimated resale value is $63,281.25. Choice C.