Answer to Question #91274 in Algebra for Emma Weaver

Question

A water tank has 8 feet of water in it. At the end of each hour the water level falls to 75% of the previous level. Identify the graph of the sequence and the correct description of its pattern. Then identify the what the water level will be after 6 hours.

Answer 1

1) Let An is the level of water after n haours. Then:

A₀ = 8 feet,

A₁ = A₀ * 75/100 = 8 * 3/4 = 6;

A₂ = A₁ * 3/4 = 6 * 3/4 = 9/2 = 4 1/2;

A₃ = A₂ * 3/4 = 9/2 * 3/4 = 27/8 = 3 3/8;

A₄ = A₃ * 3/4 = 27/8 * 3/4 = 81/32 = 2 17/32;

A₅ = A₄ * 3/4 = 81/32 * 3/4 = 243/128 = 1 115/128;

A₆ = A₅ * 3/4 = 243/128 * 3/4 = 729/512 = 1 217/512 (feet).

2) The common formula for the water level after n haours is:

An = 8 * (3/4)ⁿ.

This is the exponential decay with the base 3/4. All the points on a line that graphs the pattern are accurate:

3) Thus, the water level after 6 hours will be:

 A₆ ≈ 1,423 feet.