Subjects algebra

Price Change

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Price Change


1. The problem states that the price of softwood increased 6% annually for the last 5 years and before that, it had decreased by 2% annually. 2. Let's denote the price at the initial time (before the 5 years of increase) as $P_0$. 3. The price after the period of decrease is $P_1 = P_0 \times (1 - 0.02)^t$ where $t$ is the number of years of decrease before the increase period. 4. Then, the price increased for 5 years at 6% per annum, so the price after 5 years is given by: $$P = P_1 \times (1 + 0.06)^5$$ 5. Substituting $P_1$ into the expression: $$P = P_0 \times (1 - 0.02)^t \times (1 + 0.06)^5$$ 6. Without the exact number of years $t$ for the decrease period, we cannot find a numeric final price but this formula expresses the relationship. 7. If $t$ is given, substitute to find the multiplier effect on the initial price. In summary, the price after these changes is $$P = P_0 \times (0.98)^t \times (1.06)^5$$