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A nautilus shell is made up of many chambers, each chamber roughly 5%5\% larger than the previous one. Assuming a nautilus creates a new chamber every year, and this year's chamber has a volume of 880880 microliters, how large will the chamber created in 88 years be? If necessary, round your answer to the nearest tenth.\newline\newline____ microliters\newline

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Q. A nautilus shell is made up of many chambers, each chamber roughly 5%5\% larger than the previous one. Assuming a nautilus creates a new chamber every year, and this year's chamber has a volume of 880880 microliters, how large will the chamber created in 88 years be? If necessary, round your answer to the nearest tenth.\newline\newline____ microliters\newline
  1. Identify initial volume and growth rate: Identify the initial volume and the rate of growth.\newlineThe initial volume of the chamber is 880880 microliters, and the rate of growth is 5%5\% larger than the previous one each year.
  2. Convert percentage growth to decimal: Convert the percentage growth to a decimal.\newlineTo work with the percentage in calculations, convert it to a decimal. A 5%5\% increase is the same as multiplying by 1.051.05 (since 5%5\% as a decimal is 0.050.05, and you add this to 11 to account for the original volume).
  3. Determine formula for volume: Determine the formula for the volume after a certain number of years.\newlineThe formula for the volume after nn years, given a constant percentage increase, is V(n)=V(0)×(1+r)nV(n) = V(0) \times (1 + r)^n, where V(0)V(0) is the initial volume, rr is the rate of growth as a decimal, and nn is the number of years.
  4. Substitute values into formula: Substitute the known values into the formula. V(8)=880×(1.05)8V(8) = 880 \times (1.05)^8
  5. Calculate volume after 88 years: Calculate the volume after 88 years.\newlineV(8)=880×(1.05)8V(8) = 880 \times (1.05)^8\newlineUsing a calculator, we find:\newlineV(8)≈880×1.477455V(8) \approx 880 \times 1.477455\newlineV(8)≈1300.1604V(8) \approx 1300.1604 microliters
  6. Round answer to nearest tenth: Round the answer to the nearest tenth.\newlineThe volume of the chamber created in 88 years, rounded to the nearest tenth, is approximately 1300.21300.2 microliters.

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