COMPLETE ALL. THEY MUST HAVE STEP BY STEP WITH EXPLANATIONS.

ORIGINAL ANSWERS

I WILL GIVE GOOD OR BAD FEEDBACK BASED ON THE FINAL SCORE. SO PLEASE TUTORS DO YOUR BEST, I NEED EXPERTS ON CALCULUS HERE, TAKE YOUR TIME BUT DO IT EXCELLENT. THANK YOU

2 In a solar sysmm, two comets pass near the sun, which is located at the origin. Comet E is modeled by \"Eff +%-1 and Comet H is modeled by (x1113): _% -1. where all measurements are in astronomical unils. Part A: What are the vertices for the path of Comet E? Show your work. (4 points) Part B: Which comet travels closer to the sun? Give evidence to support your answer. (5 points) Part C: What key feature does the sun represent for both comets? Give evidence in support your answer, (6 points) Lionsh are considered an invasive species, with an annual growth rate of 67%. Ascientist estimates there are 8,000 lionfish in a certain bay alter the rst year. Part: A: Write the explicit equation for Mn} that represents the number ot lionfrsh in the bay alter .0 years. Show all necessary math work. (4 points) Part B: How many Iionlish will be in the bay atter 6 years? Round to the nearest whole number and show all necessary math work. (3 points) Part: C: It scientists remove 1,200 fish per year from the bay after the rst year, what is the recursive equation for n)? Show all necessary math work (3 points The sequence 1. _; 3 4 - - _ __ IS men. 3 9' 9 Part A: Msuming the pattern continues. list the next four terms in the sequence. Show all necessary math work. (4 points) Part B: Write the explicit equation for f (n) to represent the sequence. Show all necessary math work. (4 points) Part C: Is the sign of f (53) positive or negative? Justify your reasoning mathematically without determining the value of f (53). (2 points) An applicant receives a job offer from two different companies. Offer A is a starting salary of $54,000 and a 6% increase for 5 years. Offer B is a starting salary of $54,000 and an increase of $3,000 per year Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation for An that represents the total salary received after n years. Justify your reasoning mathematically. (3 points) Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for B, that represents the total salary received after n years. Justify your reasoning mathematically. (3 points) Part C: Which offer will provide a greater total income after 5 years? Show all necessary math work. (4 points) An applicant receives a job offer from two different companies. Offer A is a starting salary of $54,000 and a 6% increase for 5 years. Offer B is a starting salary of $54,000 and an increase of $3,000 per year. Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation for An that represents the total salary received after n years. Justify your reasoning mathematically. (3 points) Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for B, that represents the total salary received after n years. Justify your reasoning mathematically. (3 points) Part C: Which offer will provide a greater total income after 5 years? Show all necessary math work. (4 points) A hiker on the Appalachian Trail planned to increase the distance covered by 20% each day. After 7 days, the total distance traveled is 51.664 miles. Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points) Part B: What is the equation for Sn? Show all necessary math work. (3 points) Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work