Algebra 2: Suzy has a transparent ballpoint pen in which she can see its ink level...

Question

Suzy has a transparent ballpoint pen in which she can see its ink level. After two weeks of use, she notices that she has 7 cm of ink left in the pen. After four weeks, she has 6 cm of ink left in the pen. After eight weeks, she has 4 cm of ink left in the pen. Suzy presumes she is using the same amount of ink cach week.

a) If Suzy's presumption is correct, how much ink was in the pen when she started using it?

b) Write an equation that models the length of ink in Suzy's pen each week. Define your variables.

c) If she continues this pattern of use, for how many total weeks will Suzy be able to use her pen? Justify your answer.

Answer 1

This is a linear equation. From the description 7 cm after 2 weeks, y₁ = 7 and x₁ = 2 and

6 cm after 4 weeks, y₂ = 6 and x₂ = 4

The point slope form is:

y - y₁ = m(x-x₁) where m = (y₂-y₁)/(x₂-x_{1) = (6-7)/(4-2) = -1/2}

_{So y = (-1/2)(x - 2) + 7 = -x/2 + 8}

_{a) y = f(x), f(0) = (-1/2)(0) + 8 = 8 cm}

_{b) y = (-1/2)x + 8 where x = weeks and y = ink length}

_{c) Solve for x: -x/2 + 8 = 0 x = 2•8 = 16 weeks}