An exponential model multiplies a starting amount by the same factor each time the exponent increases by . If the question gives you a function and asks for its value after a stated time, define the rule in Desmos and evaluate it at that time. A factor below is the part kept, not a fixed amount lost. Use the requested time as the input, and let the exponent count the multiplications.
Hints
- Hint 1
In function notation, the number inside is the time you put into the rule. The question asks for the value after two years. What number belongs inside the parentheses?
- Hint 2
In an exponential model, the exponent counts repeated multiplications by the same factor. After two years, how many times does the factor multiply the starting value?
Step-by-step
Evaluate the model in Desmos
Step 1Turn the time into a function input
The input counts years after purchase, so 2 years means find . Put in for :
- Step 2
Define the given function
Type in Desmos. It graphs a decreasing curve. The factor means the laptop keeps 75% of its previous value each year, rather than losing the same dollar amount each year.
- Step 3
Read the two-year value
Type on the next line. Desmos prints , the output after the factor has been applied twice. So the laptop will be worth $450 two years after purchase. Choice D.