Slide 2 – Matching Challenge

• Input function F(t) = 25000*.85^(t)

• Using V(t), determine what values of a and b match the target depreciation model?

• a =? b =?
  
  

Slide 3 – Reflect & Explain (Interpretation)

In the equation V(t)=a*(b)^t

• What does the number a represent? (Explain what a represents in this context.)

• What does b represent? (Explain how changing b affects depreciation.)

  • If b = 1, what would the graph look like?

• Write a short interpretation in your own words explaining.
  
  

Slide 4 – Create Your Own

• Redefine V(t) = a*b^(t)

  • Designate values for a and b. No sliders.

  • Add a table for (t, V(t)) for values ranging from 0 to 10.

• Choose a realistic car price for a and a rate b (like 0.9 or 0.8).

• Fill in your table and describe how quickly the car loses value. 

Desmos allows students to visualize parameter sensitivity. For instance, decreasing b to 0.6 shows more rapid depreciation, which they can connect to poorer car investment. Increasing a simulates buying a more expensive car. 

• Explore with Google Sheets and compare. (see actvity below)

  • What differences do you notice from this platform compared to Desmos?