Math Problem Statement

. An Arctic ice study found that in the summer, 70% of an ocean region was ice covered. The study also predicted the region’s ice would be reduced by 6% per year. a) What percent of the region will be ice covered after the fi rst year? Express your answer to the nearest tenth of a percent. b) What percent of the region will be ice covered after the third year? Express your answer to the nearest tenth of a percent. c) How many years will pass before less than one half of the region is covered by ice?

Solution

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Math Problem Analysis

Mathematical Concepts

Exponential Decay
Algebra
Logarithms

Formulas

P_n = P_0 × (0.94)^n
n < ln(0.7143) / ln(0.94)

Theorems

Exponential Decay Formula
Logarithmic Transformation

Suitable Grade Level

Grades 10-12