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In the town of Lakemont (population = 10,000), 200 people were living with chronic hepatitis B at the beginning of 2025.During the year 2025, 50 new cases of hepatitis B were diagnosed. Calculate the incidence rate of hepatitis B for 2025. (You may use the online calculator here in the exam.  Express your answers as percentages or per 1,000 people.)

Question 1 : (4 points)The power series converges on [-2.4][-2.4] where the coefficient should be 1. Find the center and radius of convergence. Write the power series in standard form with the correct radius of convergence.Question 2:  (4 points) You are given the Maclaurin Series ,  11+x2=∑n=0∞(-1)nx2n \frac{1}{1+x^2}= \sum_{n=0}^{\infty}(-1)^nx^{2n} , |x|0Show that bnb_{n} is decreasing sequence. Find the limit of bn b_n State whether the series converges or diverges. Determine whether the convergence is absolute or conditional.Question 8: (8 points)Find the radius and interval of convergence of the series ∑n=0∞n!(x+1)n7n \sum_{n =0}^{\infty} \frac{n! (x+1)^n}{7^n} Question 9: (8 points)Consider the series f(x)=x2e-2x f(x) = x^2 e^{-2x}  . Using ex=∑n=0∞xnn! e^x = \sum_{n =0}^{\infty} \frac{x^n}{n!} Find the Maclaurin series for f(x)f(x) Compute f(10)(0) f^{(10)} (0) and simplify your answer.Question 10: (6 points)You are given the Maclaurin series for cosx \cos x : sinx=∑n=0∞(-1)n(2n+1)!x2n+1 \sin x = \sum_{n=0}^{\infty} \frac{(-1)^n }{(2n+1)!} x^{2n+1} Differentiate the given series term by term.Identify the function the new series represents.Find the sum of the series. ∑n=0∞(-1)n22n(2n+1)! \sum_{n=0}^{\infty} \frac{(-1)^n 2^{2n}}{(2n+1)!} Question 11: (6 points) Find the area under the curve y=cosx y =\cos x from to x=0 x =0 to x=πx=\pi (6 points) Find the volume of the solid generated by rotating the region bounded by y=cosx y =\cos x , x=0 x =0 and y=0y =0 about the x-axis.(8 points) Find the volume of the solid generated by rotating the region bounded by y=cosx y =\cos x , x=0 x =0 and y=0y =0 about the y-axis.

Short answer question: Pretend that you are a self-identified male older adult shopping for OTC medicines to restock in your home for common, minor health issues. You have high blood pressure and an enlarged prostate (benign prostatic hyperplasia, or BPH), and you’ve had several falls recently. Based on your health conditions and fall history, what is one (1) OTC medicine or ingredient you should avoid, and why could it be risky for you? (one-half point for the medicine/ingredient & one-half point for “why”; 1 point total possible)

A 30 year old woman is a body mass index (BMI) greater than 30 who is seeking Plan B One-Step (levonorgestrel) after unprotected intercourse two days ago. She recently lost her job and currently lacks health insurance. Which statement includes the correct key points regarding this person’s use of Plan B?

Short answer question: Which two (2) OTC drugs are included in the 20 most frequently reported medications associated with serious adverse outcomes in children ages 1 to less than 18 years? (Only state 2 drugs; one-half point per drug)

Extra credit question (optional) Think about all the lecture topics for this exam:  pediatric issues older adults skin conditions (burns, acne, allergic contact dermatitis) vitamins & nutritional supplements vaccination menstruation & pregnancy prevention What is one (1) thing you learned (from any one of the lecture topics) that most surprised you? (Note: only the first item typed will be considered, so only type 1 thing)

An adult returned home yesterday from a late fall camping trip where he went hiking through woods and prairies that don’t have trails.  The weather was warm, and he chose to wear cargo shorts instead of long pants, though he did wear hiking boots.  Today, he has an angry red rash on both his lower legs below his knees that is very pruritic (itchy), and some blisters are starting to form.  He’s fairly certain he must have hiked through poison ivy vines since he’s had a rash like this before from that plant. Which of the following would be the best thing for this adult to do for self-care at this time?

Which of the following is true based on the older adults lecture? (Select all that apply)

Which of the following topics is not covered in the “Kids Aren’t Just Small Adults” required reading?

An adult is taking care of her 3-year-old nephew for the weekend.  The child takes a single daily dose of OTC allergy medicine, but his mom forgot to pack the dosing device with the medicine.  What would be the best way for the adult to give her nephew his OTC allergy medicine tomorrow?