Let's Practice One of These
Tangier Island is an island in Virginia that was once home to over 1000 residents. Unfortunately, the island has been shrinking since approximately 1800. In 1850 (𝑡=50), the island had an area of 2163 acres. In 2013 (𝑡=213), the island had an area of 789 acreas.
The area of Tangier Island can be modelled by the function 𝑆𝑡=𝑎𝑡1.6+𝑏.
B(i) Use the given data to find the average rate of change of the area of the island, in acres per year, from 𝑡=50 to 𝑡=213. Express your answer as a decimal approximation. Show the computations that lead to your answr.
B(ii) Use the average rate of change found in B(i) to estimate the area of the island for 𝑡=250. Show the work that leads to your answer.
B(iii) Use concavity to explain why the approximation found in B(ii) is an overestimate of the value of 𝑆250.