Question

At time t​=0, water begins to drip out of a pipe into an empty bucket. After ​minutes, there are 7 inches of water in the bucket. Write a linear function rule to model how many inches of water w are in the bucket after 49 any number of minutes t.

Answer 1

The answer is the answer I had it on a test

Answer 2

Let's call the rate at which water drips into the bucket "r". Then we can write the function rule for the number of inches of water in the bucket after t minutes as w = rt + b.

We know two things:

At t = 0, there are 0 inches of water in the bucket, so w = r * 0 + b = b.

After 7 minutes, there are 7 inches of water in the bucket, so w = r * 7 + b = 7.

Using these two points, we can solve for b and r:

b = 0

r = 7 / 7 = 1

So our function rule for the number of inches of water in the bucket after t minutes is:

w = rt + b = 1t + 0 = t.

Now, to find out how many inches of water are in the bucket after 49 minutes, we can plug in t = 49:

w = 49 * 1 + 0 = 49

So there are 49 inches of water in the bucket after 49 minutes.