Unit 2A Practice FRQ Questions for Exam 2B

University:
The Pennsylvania State University
Course:
STAT 200 | Elementary Statistics
Academic year:

2024
Views:

306

Pages:

2
Author:

Taha Tayfur

AP Precalculus Practice FRQ Questions for Exam 2B. Calculator Allowed. Round decimals to thousandths place or more. 𝑡 (years since 2006) 0 2 4 6 8 10 12 𝐷(𝑡) (deaths in thousands) 590 511 455 384 339 295 275 1. The number of worldwide deaths of children under five years old due to malaria has been decreasing in recent years. The table above gives the yearly number of deaths (in thousands) for children under five years old due to malaria for several years since 2006. (A) (i) Use the data in the table to create an exponential function model of the form 𝑦 = 𝑎𝑏 𝑥 , where 𝑦 represents the number of deaths (in thousands) 𝑥 years since 2006. (ii) Based on the regression model from part (i), how many thousands of children under five years old are predicted to die from malaria in the year 2030? (iii) Find the residual value of the number of malaria deaths when 𝑡 = 8. Does this residual value indicate that our model overestimated or underestimated the number of malaria deaths when 𝑡 = 8? Give a reason for your answer. (B) (i) The function 𝐷(𝑡) can also be modeled with a quadratic function. Let 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 be the quadratic regression model for 𝐷(𝑡). Use the data in the table to find the quadratic regression model for 𝑃(𝑡). (ii) Find the value of 𝐷(18) predicted by the quadratic regression model. (C) (i) The graphs of the residuals for the exponential and quadratic regression models are below. Use the graphs of the residuals to determine which model was appropriate for the data. Explain your reasoning. Quadratic Regression Model Residuals Exponential Regression Model Residuals Years since 2006 Years since 2006 𝑛 1 4 5 𝑓𝑛 243 𝑘 3 2. The table above presents values for a sequence 𝑓 at selected values of 𝑛, where 𝑘 is a constant. The data in the table can be used to find two models for 𝑓𝑛 : an arithmetic model (𝑎𝑛 ) and a geometric model (𝑔𝑛 ). (A) (i) The arithmetic model 𝑎𝑛 for 𝑓𝑛 can be written as 𝑎𝑛 = 𝑎0 + 𝑑𝑛, where 𝑑is the common difference between successive terms. Use the data in the table to find an expression for 𝑎𝑛 . (ii) Using the arithmetic model 𝑎𝑛 , find the value of the constant 𝑘in the table above. (iii) According to the arithmetic model, for what value of 𝑛 will 𝑓𝑛 = −117? Show the work that leads to your answer. (B) (i) The geometric model 𝑔𝑛 for 𝑓𝑛 can be written as 𝑔𝑛 = 𝑎𝑏 𝑛 , where 𝑎and 𝑏are constants. Use the given data to write two equations that can be used to find the values for constants 𝑎and 𝑏in the expression for 𝑔𝑛 . (ii) Find the values for 𝑎and 𝑏. (iii) Using the geometric model 𝑔𝑛 , find the value of the constant 𝑘in the table above. (C) (i) For 𝑛 ≥ 0, the value of 𝑓𝑛+1 𝑓𝑛 remains constant as 𝑛 increases. Based on this, is 𝑎𝑛 or 𝑔𝑛 a better model for 𝑓𝑛 ? Give a reason for your answer.

Unit 2A Practice FRQ Questions for Exam 2B

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