Concept explainers
Alzheimer’s Disease Partially because of American living longer, the number with Alzheimer’s disease and other dementia is projected to grow each year. The table below gives the millions of U.S. citizen with Alzheimer’s from 2000 and projected to 2050.
(Source: National Academy on an Aging Society)
a. Create a
b. Find a quadratic function that models this data. Report the model with four significant digits.
c. Graph the data and the model on the same axes, and comment on the fit.
d. How many Americans does the model predict will have Alzheimer’s disease or other dementia 2056?
e. In what year after 2000 does the model predict that 10.2 million Americans will have Alzheimer’s or other dementia?
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COLLEGE ALGEBRA IN CONTEXT W/ INT. REVIE
- 2. (i) Which of the following statements are true? Construct coun- terexamples for those that are false. (a) sequence. Every bounded sequence (x(n)) nEN C RN has a convergent sub- (b) (c) (d) Every sequence (x(n)) nEN C RN has a convergent subsequence. Every convergent sequence (x(n)) nEN C RN is bounded. Every bounded sequence (x(n)) EN CRN converges. nЄN (e) If a sequence (xn)nEN C RN has a convergent subsequence, then (xn)nEN is convergent. [10 Marks] (ii) Give an example of a sequence (x(n))nEN CR2 which is located on the parabola x2 = x², contains infinitely many different points and converges to the limit x = (2,4). [5 Marks]arrow_forward2. (i) What does it mean to say that a sequence (x(n)) nEN CR2 converges to the limit x E R²? [1 Mark] (ii) Prove that if a set ECR2 is closed then every convergent sequence (x(n))nen in E has its limit in E, that is (x(n)) CE and x() x x = E. [5 Marks] (iii) which is located on the parabola x2 = = x x4, contains a subsequence that Give an example of an unbounded sequence (r(n)) nEN CR2 (2, 16) and such that x(i) converges to the limit x = (2, 16) and such that x(i) # x() for any i j. [4 Marksarrow_forward1. (i) which are not. Identify which of the following subsets of R2 are open and (a) A = (1, 3) x (1,2) (b) B = (1,3) x {1,2} (c) C = AUB (ii) Provide a sketch and a brief explanation to each of your answers. [6 Marks] Give an example of a bounded set in R2 which is not open. (iii) [2 Marks] Give an example of an open set in R2 which is not bounded. [2 Marks]arrow_forward
- sat Pie Joday) B rove: ABCB. Step 1 Statement D is the midpoint of AC ED FD ZEDAZFDC Reason Given 2 ADDC Select a Reason... A OBB hp B E F D Carrow_forward2. if limit. Recall that a sequence (x(n)) CR2 converges to the limit x = R² lim ||x(n)x|| = 0. 818 - (i) Prove that a convergent sequence (x(n)) has at most one [4 Marks] (ii) Give an example of a bounded sequence (x(n)) CR2 that has no limit and has accumulation points (1, 0) and (0, 1) [3 Marks] (iii) Give an example of a sequence (x(n))neN CR2 which is located on the hyperbola x2 1/x1, contains infinitely many different Total marks 10 points and converges to the limit x = (2, 1/2). [3 Marks]arrow_forward3. (i) Consider a mapping F: RN Rm. Explain in your own words the relationship between the existence of all partial derivatives of F and dif- ferentiability of F at a point x = RN. (ii) [3 Marks] Calculate the gradient of the following function f: R2 → R, f(x) = ||x||3, Total marks 10 where ||x|| = √√√x² + x/2. [7 Marks]arrow_forward
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- Use the graphs to find estimates for the solutions of the simultaneous equations.arrow_forwardPLEASE SOLVE STEP BY STEP WITHOUT ARTIFICIAL INTELLIGENCE OR CHATGPT SOLVE BY HAND STEP BY STEParrow_forward6) Find the area of the shaded region. Leave your answer in terms of π. A 2 B C A) 16.5л B) 30д 3.1988 C) 3л π D) 7.5π 9.+2uarrow_forward
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