Question

Suppose a balloon is filled with 5000 cm³ of helium. It then loses one fourth of its helium each day. How much helium will be left in the balloon at the start of the tenth day?c. How can you write a formula for this sequence?

Answer 1

The sequence can be expressed by the formula: v(n) = 5000 . (3/4)ⁿ⁻¹. Helium left at the start of the 10th day is 375.42 cm³

1st day:

Helium is filled with 5000 cm³ of helium.

We can write v(1) = 5000 cm³

2nd day:

The balloon losses 1/4 of helium volume. In other word, the remaining volume of helium is:

(1 - 1/4) = 3/4 of its initial volume.

We can write:

v(2) = 3/4 . 5000 = 3750  cm³

We can continue this process:

v(3) = 3/4 . 3750 = 2812.5

Notice that each day remaining volume of helium forms a geometric sequence, with v(1) = 5000 and a common ratio (r) = 3/4.

Recall the formula for the nth term of a geometric sequence:

v(n) = v(1) . rⁿ⁻¹

To find the explicit formula, substitute v(1) = 5000 and (r) = 3/4:

v(n) = 5000 . (3/4)ⁿ⁻¹

Tenth day means n = 10. Substitute these parameters into the formula:

v(10) = 5000 . (3/4)¹⁰⁻¹

v(10) = 5000 . (3/4)⁹

        = 375.42 cm³

Learn more about geometric sequence here:

brainly.com/question/23709259

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