Question

A nautilus shell is made up of many chambers, each chamber roughly 6% larger than the previous one. Assuming a nautilus creates a new chamber every year, and this year's chamber has a volume of 991 microliters, how large will the chamber created in 9 years be?

Answer 1

Explanation:

Let's assume that the current chamber has a volume of V0 = 991 microliters, and each new chamber has a volume 6% larger than the previous one. Then, the volume of the chamber created after one year will be:

V1 = V0 + 0.06 * V0 = 1.06 * V0

Similarly, the volume of the chamber created after two years will be:

V2 = V1 + 0.06 * V1 = 1.06 * V1 = 1.06 * 1.06 * V0

In general, the volume of the chamber created after n years will be:

Vn = (1.06)^n * V0

Therefore, the volume of the chamber created after 9 years will be:

V9 = (1.06)^9 * V0 = 1.06^9 * 991 microliters

Using a calculator, we find that V9 is approximately 1,711.94 microliters. Therefore, the chamber created in 9 years will have a volume of approximately 1,711.94 microliters