Answer to Question #90415 in Algebra for Kate Kishpaugh

Question

A water tank has a bit 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 what the water level will be after six hours

Answer 1

This is a geometric progression

b₁ = 1 (first term);

b₂ = 1 * 0.75 = 0.75;

b₃ = 1 * (0.75)²;

....

b_n = 1 *(0.75)^n-1 .

The pattern is

y(x)=(0.75)^x-1 (decreasing exponential function).

After six hours the water level will be

b₆ = 1 * (0.75)⁵ = 0.2373 = 24%.