Suppose a person’s body burns 130 kcal per week for each pound it weighs. Suppos

Question

Suppose a person’s body burns 130 kcal per week for each pound it weighs. Suppose this person presently weighs 165 pounds and consumes about 21,000 kcal per week. Suppose this person decides to eat 200 kcal less each week than the week before. Let c(n) represent the number of kilocalories this person consumes during the n-th week of this diet. Develop a dynamical system of two equations, one for c(n) and one for w(n), assuming c(1) = 20,800 and w(0) = 165 (to work this problem, you need to know that burning 3600 kcal would reduce a person’s weight by 1 pound and consuming 3600 kcal would result in the gaining of 1 pound).

Explanation / Answer

the calorie intake is decreasing by 200 Kcal every passing week.

the person starts with 20800 Kcal and the following week he'll take 20600 Kcalories

so the sequence that we'll get will be in an arithmetic progression

20800 , 20600 ,20400 , 20200,..............

the nth term of the above sequence would be the number of calories consumed by the person in the nth week.

the common difference is (d) = -200

the first term is = 20800

=> C(n) = the number of kilocalories this person consumes during the n-th week of this diet

C(n) = a + (n-1)d

C(n) = 20800 + (n-1)(-200)

C(n) = 21000 - 200n       

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