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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?

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Answer:

c = 8.14 million×(0.9166)^t

4.83 million  

Step-by-step explanation:

Data:

  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.

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