Question

graham uses a 10 by 10 grid to model a decreasing pattern. he cuts off a section representing a percent of the current area so that the remaining area represents the next term in the pattern, rounded to nearest whole centimeter. the area after each cut is shown on the graph. after each cut, what percentage of the previous area is the the remaining area? 10% 20% 80% 100%

Explanation:

Step1: Calculate the ratio of consecutive areas

Let's take two consecutive points. For example, if the first - area \(A_1 = 80\) (when \(x = 1\)) and the second - area \(A_2=64\) (when \(x = 2\)). The formula for the percentage \(p\) of the previous area that the remaining area represents is \(p=\frac{A_{n + 1}}{A_n}\times100\%\).
Substitute \(A_1 = 80\) and \(A_2 = 64\) into the formula: \(\frac{64}{80}\times100\%=0.8\times100\% = 80\%\).
We can check another pair. If \(A_2 = 64\) and \(A_3 = 51\) (approximate value from the graph), \(\frac{51}{64}\times100\%\approx0.8\times100\%=80\%\) (since \(51\approx64\times0.8\)).

Answer:

80%