Question

ivan is adding water to a swimming pool at a constant rate. the table below shows the amount of water in the pool after different amounts of time. time (minutes) water (gallons) 8 153 12 197 16 241 20 285 answer the following questions. (a) choose the statement that best describes how the time and the amount of water in the pool are related. then give the value requested. ∘ as time increases, the amount of water in the pool decreases. at what rate is the amount of water in the pool decreasing? gallons per minute ∘ as time increases, the amount of water in the pool increases. at what rate is the amount of water in the pool increasing? gallons per minute (b) how much water was already in the pool when ivan started adding water? gallons

Explanation:

Part (a) - Rate of Increase

Step1: Identify two points

We can take two points from the table, e.g., (8, 153) and (12, 197).

Step2: Calculate the rate

The rate of change (slope) is given by $\frac{\Delta y}{\Delta x}=\frac{197 - 153}{12 - 8}=\frac{44}{4} = 11$.

Step1: Use the linear equation

The linear equation is $y = mx + b$, where $m = 11$ (rate from part a), and we can use a point, say (8, 153).

Step2: Solve for $b$

Substitute into the equation: $153=11\times8 + b$. So, $153 = 88 + b$. Then, $b=153 - 88 = 65$.

Answer:

The rate at which the amount of water in the pool is increasing is 11 gallons per minute.

Part (b) - Initial Amount of Water