Section II Part A — Full Practice Exam 2

Questions in this quiz (1)

1. As a result of improvements in technology, the average internet speed has been increasing over time. In the year $$2000$$ $$(t=0)$$, the average speed was $$1.5$$ Mbps. In the year $$2020$$ $$(t=20)$$, the average speed was $$25.3$$ Mbps. The average internet speed in a given year can be modeled by the function $$S$$, given by $$S(t)=a+b\ln(t+1),$$ where $$S(t)$$ is the average speed in Mbps, and $$t$$ is the number of years since $$2000$$. (A) (i) Use the given data to write two equations that can be used to find the values of constants $$a$$ and $$b$$ in the expression for $$S(t)$$. (ii) Find the values for $$a$$ and $$b$$ as decimal approximations. (B) (i) Use the given data to find the average rate of change of the average internet speed, in Mbps per year, from $$t=0$$ to $$t=20$$. Express your answer as a decimal approximation. Show the computations that lead to your answer. (ii) Interpret the meaning of your answer from part (i) based on the context of the problem. (iii) Use the average rate of change found in part (i) to estimate the average internet speed in the year $$2010$$. Show the work that leads to your answer.

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