The iPad was introduced in 2010. Five years later (𝑡=5), 54.9 million iPads were sold. Three years after that (𝑡=8), 43.5 million iPads were sold. After that, Apple no longer shared sales numbers, but industry trackers believe that in 2023 (𝑡=13), 54.1 million iPads were sold.
The number of iPads sold can be modelled by 𝑆𝑡=𝑎𝑡3+𝑏𝑡2+𝑐𝑡+7.5, where 𝑆𝑡 is the number of iPads sold, in millions, 𝑡 years after the launch of the product.
Use the given data to find the average rate of change of the number of iPads sold, in millions, from 𝑡=8 to 𝑡=13. Express your answer as a decimal approximation. Show the computations that lead to your answer.
Use 𝑆13 and the average rate of change found in part C to estimate the number of iPads that will be sold in 2025 (𝑡=15). Show the work that leads to your answer.
Does the value found in part D overestimate or underestimate the value of 𝑆15? Use the concavity of the graph of 𝑆𝑡 to explain why this is the case.