A bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. The tire pressure is currently 1,060 kilopascals. What will it be in 4 minutes?If necessary, round your answer to the nearest tenth.
Question
A bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. The tire pressure is currently 1,060 kilopascals. What will it be in 4 minutes?If necessary, round your answer to the nearest tenth.
Solution
To solve this problem, we need to calculate the tire pressure after each minute for 4 minutes.
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After the first minute, the tire will lose 10% of its pressure. So, we calculate 10% of 1,060 kilopascals: 0.10 * 1,060 = 106 kilopascals. We subtract this from the initial pressure: 1,060 - 106 = 954 kilopascals.
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After the second minute, the tire will lose 10% of its new pressure. So, we calculate 10% of 954 kilopascals: 0.10 * 954 = 95.4 kilopascals. We subtract this from the pressure after the first minute: 954 - 95.4 = 858.6 kilopascals.
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After the third minute, the tire will lose 10% of its new pressure. So, we calculate 10% of 858.6 kilopascals: 0.10 * 858.6 = 85.86 kilopascals. We subtract this from the pressure after the second minute: 858.6 - 85.86 = 772.74 kilopascals.
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After the fourth minute, the tire will lose 10% of its new pressure. So, we calculate 10% of 772.74 kilopascals: 0.10 * 772.74 = 77.274 kilopascals. We subtract this from the pressure after the third minute: 772.74 - 77.274 = 695.466 kilopascals.
So, after 4 minutes, the tire pressure will be approximately 695.5 kilopascals, rounded to the nearest tenth.
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