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Creep is the ratio of elongation to original length that occurs in materials over time. For a particular steel structure, for the first 50 days the creep increases by 6×10^(-6) per day. After the 50th day, when the creep is 3×10^(-4), the creep triples every 62 days. After the 236 th day, how much less would the creep be if it had continued to grow linearly after the 50 th day? Choose 1 answer: (A) 1.1 ×10^(-3) (B) 1.4 ×10^(-3) (c) 6.7 ×10^(-3) (D) 8.1 ×10^(-3)

Creep is the ratio of elongation to original length that occurs in materials over time. For a particular steel structure, for the first 5050 days the creep increases by 6×10−6 6 \times 10^{-6} per day. After the 5050 th day, when the creep is 3×10−4 3 \times 10^{-4} , the creep triples every 6262 days. After the 236236 th day, how much less would the creep be if it had continued to grow linearly after the 5050 th day?\newlineChoose 11 answer:\newline(A) 1.1×10−3 1.1 \times 10^{-3} \newline(B) 1.4×10−3 1.4 \times 10^{-3} \newline(C) 6.7×10−3 6.7 \times 10^{-3} \newline(D) 8.1×10−3 8.1 \times 10^{-3}

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Q. Creep is the ratio of elongation to original length that occurs in materials over time. For a particular steel structure, for the first 5050 days the creep increases by 6×10−6 6 \times 10^{-6} per day. After the 5050 th day, when the creep is 3×10−4 3 \times 10^{-4} , the creep triples every 6262 days. After the 236236 th day, how much less would the creep be if it had continued to grow linearly after the 5050 th day?\newlineChoose 11 answer:\newline(A) 1.1×10−3 1.1 \times 10^{-3} \newline(B) 1.4×10−3 1.4 \times 10^{-3} \newline(C) 6.7×10−3 6.7 \times 10^{-3} \newline(D) 8.1×10−3 8.1 \times 10^{-3}
  1. Calculate total creep after 236236 days: First, let's calculate the total creep after 236236 days if it had continued to grow linearly at the rate of 6×10−66\times10^{-6} per day after the 5050th day.\newlineLinear growth for the first 5050 days = 5050 days ×6×10−6\times 6\times10^{-6} per day = 3×10−43\times10^{-4}\newlineLinear growth from day 5151 to day 236236 = (236−50)(236 - 50) days ×6×10−6\times 6\times10^{-6} per day
  2. Calculate linear growth from day 5151 to day 236236: Now, let's perform the calculation for the linear growth from day 5151 to day 236236. Linear growth from day 5151 to day 236236 = 186186 days ×6×10−6\times 6\times10^{-6} per day = 1116×10−61116\times10^{-6} = 1.116×10−31.116\times10^{-3}
  3. Add linear growth for the first 5050 days to linear growth from day 5151 to day 236236: Next, we add the linear growth for the first 5050 days to the linear growth from day 5151 to day 236236 to get the total linear creep after 236236 days.\newlineTotal linear creep after 236236 days = 3×10−4+1.116×10−3=1.416×10−33\times10^{-4} + 1.116\times10^{-3} = 1.416\times10^{-3}
  4. Calculate actual creep after 236236 days: Now, let's calculate the actual creep after 236236 days. We know that after the 5050th day, the creep is 3×10−43\times10^{-4} and it triples every 6262 days.\newlineThe number of 6262-day periods after the 5050th day until the 236236th day = (236−50)/62=186/62=3(236 - 50) / 62 = 186 / 62 = 3 periods
  5. Triple the creep value: Since the creep triples every 6262 days, we need to triple the creep value 33 times.\newlineActual creep after 236236 days = 3×10−4×33=3×10−4×27=81×10−4=8.1×10−33\times10^{-4} \times 3^3 = 3\times10^{-4} \times 27 = 81\times10^{-4} = 8.1\times10^{-3}
  6. Find the difference between actual creep and linear creep: Finally, we find the difference between the actual creep and the linear creep after 236236 days.\newlineDifference = Actual creep - Linear creep = 8.1×10−38.1\times10^{-3} - 1.416×10−31.416\times10^{-3} = 6.684×10−36.684\times10^{-3}
  7. Round the difference to the nearest option: We round the difference to the nearest option provided in the question.\newlineThe closest answer to 6.684×10−36.684\times10^{-3} is 6.7×10−36.7\times10^{-3}, which corresponds to option (C).

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