In 2007, there were more than 8.14 million cars for sale. Over the next 3 years, the number of cars decreased by 23%. Write an exponential growth or decay model given by the number of c cars over t years after 2007. Use this model to estimate how many cars there will be in 2013?

c = 8.14 million * (0.9166) ^t

4.83 million

Step-by-step explanation:

dа ta:

t = y - 2007

c₀ = 8.14 million

c₃ = 23 % less than c₁

Part 1. Calculate c₃

c₃ = c₀ (1 - 0.23) = 0.77c₀

Part 2. Calculate r

c₃ = c₀r^t

0.77c₀ = c₀r³

0.77 = r³ Divided each side by c₀

r = 0.9166 Took the cube root of each side

The explicit decay model is c = 8.14 million * (0.9166) ^t

Part 3. Prediction

t = 2013 - 2007 = 6

c = c₀r^t = 8.14 million * (0.9166) ⁶ = 8.14 million * 0.5929 = 4.83 million

The model predicts that there will be 4.83 million cars for sale in 2013.