Question

A nautilus shell is made up of many chambers, each chamber roughly 5% larger than the

previous one. Assuming a nautilus creates a new chamber every year, and this year's
chamber has a volume of 880 microliters, how large will the chamber created in 8 years be?
If necessary, round your answer to the nearest tenth.
microliters

Answer 1

1300.2 µL

Explanation:

You want to know the volume of a nautilus chamber in 8 years if it is 880 µL in year 0 and increases at 5% per year.

Growth factor

The growth factor is ...

growth factor = 1 + growth rate

growth factor = 1 + 0.05 = 1.05

Exponential function

Since the problem statement is about volume, we assume the growth factor applies to the chamber volume. If it applies to the linear dimension of the chamber, then the growth factor for volume will be 1.05³.

The function describing the chamber volume can be written as ...

volume = (initial volume)(growth factor)^years

In 8 years, the chamber volume will be ...

volume = (880µL)(1.05^8) ≈ 1300.2 µL

The chamber created in 8 years is expected to be 1300.2 µL.

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Additional comment

If the 5% growth rate is the rate of growth of the linear dimensions of a chamber, then its volume will grow at the rate of 1.05³ per year. In 8 years, the volume will be about 2838.1 µL.

(The wording "5% larger" is ambiguous here.)

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