Problema Solution
A puppy weighs 0.95lbs at birth, and each week he gains 24% in weight. Let An be his weight in pounds at the end of the nth week of life. Find the formula for An. How much does the puppy weigh when he is six weeks old?
Answer provided by our tutors
week n=0 when the puppy is born
A(0) = 0.95
week n=1
A(1) = A(0) + 0.24*A(0) = A(0)(1.24)
week n = 2
A(2) = A(1) + 0.24A(1) = A(1)(1 + 0.24) = A(0)(1.24)^2
week n
A(n) = A(0)(1.24)^n
we can prove this formula using Mathematical induction
the formula is true for n = 0 and lets assume the statement holds for n = k
for n = k+1 we have
A(k+1) = A(k)(1.24) = A(0)((1.24)^k)*(1.24) = A(0)(1.24)^(k+1)
the statement holds for k + 1.
The formula for A(n) is
A(n) = 0.95(1.24)^n
How much does the puppy weigh when he is six weeks old?
n = 6
A(6) = 0.95(1.24)^6
A(6) = 3.4535 lbs
after 6 weeks the puppy has 3.4535 lbs in weight.