Question

A snail travels 2 feet in 1 hour. In each subsequent hour, the snail travels two-thirds the distance it traveled in the previous hour. How far does this snail travel in 8 hours? Round your answer to the nearest tenth.

Answer 1

Answer:

The

Explanations:

The distance travelled by the snail in 1 hour = 2 feet

Let the distance travelled in 1 hour be represented by d₁

d₁ = 2 feet

The snail travelled two-thirds the distance it travelled in the previous hour

This means that the common ratio of the distance travelled is 2/3

Let the common ratio be represented as r

r = 2/3

Since the distance travelled by the snail in subsequent hours has a common ratio, r, this scenario can be modelled by the sum of n terms in a Geometric Progression.

The distance travelled by the snail in n hours will be given as:

`S_n=\text{ }(d_1(r^n-1))/(r-1)`

The distance travelled by the snail in 8 hours will be calculated by substituting n = 8 into the equation above:

`\begin{gathered} S_8=(2\lbrack((2)/(3))^8-1\rbrack)/((2)/(3)-1) \\ S_8=\text{ }(2(0.039-1))/(0.67-1) \\ S_8=\text{ }(2(-0.961))/(-0.33) \\ S_8=\text{ }(-1.922)/(-0.33) \\ S_8=5.8 \end{gathered}`

The distance travelled in 8 hours is 5.8 feet