Question

a bucket that has 3 ounces of water in it is put under a leaking ceiling. if the amount of water in the bucket doubles every minute, write a formula for how much water there will be after x hours

Answer 1

y = 120x + 3

Explanation:

1. Write out basic structure of formula

y = mx + b

y = oz. of water after x hours

m = rate of change

x = number of hours,

b = oz. of water you started with

2. Plug in what you already know

The problem states that the bucket already has 3 oz. of water, so

y = mx + 3

3. Solve for m

2 oz. of water are added to the bucket after 1 minute, making a ratio of 2:1. Since there are 60 minutes in an hour, multiply both parts of the ratio by 60 to get 120:60. This means that every 60 minutes (1 hour), 120 oz. of water are added to the bucket each hour.

4. Complete the equation

You now know that the rate of change is 120 oz. per hour, and that the bucket originally had 3 oz. of water in it, so you can complete the equation:

y = 120x + 3