Problema Solution
Laurel buys a package of pencils, and a tube of 10 refill leads. Each pencil contains 4 leads. Laurel puts the tube of refill leads into her pencil case, then adds one pencil at a time.
a) Make a table to show the number of leads in the pencil case for up to 7 pencils.
b) State the recursive rule.
c) Find the algebraic expression.
d) Find the number of leads in the pencil case for up to 24 pencils.
Answer provided by our tutors
b) the recursive rule is f(0) = 10, f(k) = f(k-1) + 4
c) lets denote
laurel puts the tube of refill leads in her case - there are 0 pencils in the bag so we can write f(0) = 10 leas in the case
laurel adds one pencil f(1) = f(0) + 4*1 = 14 leads
laurel adds another (second) pencil f(2) = f(1) + 4 = 10 + 2*4 = 18 leads
....
we can define f(k) = 10 + 4*k where k is the number of pencils added to the case
since f(k) = f(k-1) + 4 = 10 + 4(k-1) + 4 = 10 + 4*k the formula f(k) = 10 + 4*k is true.
a) k = 7 then f(7) = 10 +4*7 = 38 leads
d) f(24) = 10 + 4*24 = 106 leads