Question

Logan has an automatic hummingbird feeder in his backyard. He fills it to its capacity, 10 fluid ounces. Each day, it releases 1 fluid ounce of nectar.
Write an equation that shows how the number of fluid ounces of nectar remining, y, depends on the number of days since Logan filled it, x.

Answer 1

To create an equation that represents the relationship between the number of fluid ounces of nectar remaining \( y \) and the number of days since Logan filled the feeder \( x \), we can start with the initial condition and the rate at which the nectar is being used.

Initially, when Logan fills the feeder, it contains 10 fluid ounces. Each day, 1 fluid ounce is released, which means that for each day that passes, the amount of nectar decreases by 1 fluid ounce.

We can express this relationship with the following equation:

\[
y = 10 - x
\]

In this equation:
- \( y \) is the number of fluid ounces of nectar remaining.
- \( 10 \) is the initial amount of nectar (the capacity of the feeder).
- \( x \) is the number of days since the feeder was filled.
- Each day, \( x \) increases by 1, and consequently, \( y \) decreases by 1.

So, for any given day \( x \), you can calculate the remaining nectar by plugging the value of \( x \) into the equation.