Finding a pattern

[I jus dunno]

Hello, how do I write out this pattern

Time in Minutes	5	10	15	20	25	30	35
Bottles in Millions	2	4	6	8	10	12	14

thank you,.

 

[soroban]

Hello, I jus dunno!

How do I write out this pattern?

\(\displaystyle \begin{array}{|c||c|c|c|c|c|c|c|}\hline \text{Time in minutes} & 5 & 10 & 15 & 20 & 25 & 30 & 35 \\ \hline \text{Bottles in millions} & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\ \hline\end{array}\)

We note that: as "Time in minutes" \(\displaystyle (T)\) goes up by 5's,
. . "Bottle in millions" \(\displaystyle (B)\) goes up by 2's.


We have this chart:

\(\displaystyle \begin{array}{|c||c|c|c|c|c|c|c|}\hline \text{Time interval }(n) & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text{Time in minutes }(T) & 5 & 10 & 15 & 20 & 25 & 30 & 35 \\ \hline \text{Bottles in millions }(B) & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\ \hline\end{array}\)

We see that: .\(\displaystyle \begin{Bmatrix}T = 5n & [1] \\ B = 2n & [2] \end{Bmatrix}\)

From [1], we have: .\(\displaystyle T = 5n \quad\Rightarrow\quad n = \frac{T}{5}\)

Substitute into [2]: .\(\displaystyle B \,=\,2n\,=\,2\left(\frac{T}{5}\right) \)

Therefore: .\(\displaystyle B \:=\:\frac{2}{5}T\)

 

[I jus dunno]

Hello, I jus dunno!


We note that: as "Time in minutes" \(\displaystyle (T)\) goes up by 5's,
. . "Bottle in millions" \(\displaystyle (B)\) goes up by 2's.


We have this chart:

\(\displaystyle \begin{array}{|c||c|c|c|c|c|c|c|}\hline \text{Time interval }(n) & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text{Time in minutes }(T) & 5 & 10 & 15 & 20 & 25 & 30 & 35 \\ \hline \text{Bottles in millions }(B) & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\ \hline\end{array}\)

We see that: .\(\displaystyle \begin{Bmatrix}T = 5n & [1] \\ B = 2n & [2] \end{Bmatrix}\)

From [1], we have: .\(\displaystyle T = 5n \quad\Rightarrow\quad n = \frac{T}{5}\)

Substitute into [2]: .\(\displaystyle B \,=\,2n\,=\,2\left(\frac{T}{5}\right) \)

Therefore: .\(\displaystyle B \:=\:\frac{2}{5}T\)

Hello and thank you,

I have tried this and it definitely works for this question.
We tried a similar question

3 6 9 12 14
2 4 6 8

So, when I tried your exact equation, on the 5th term we find ourselves dividing by 3, but the answer comes up as 9.333. which really isn`t 10 as the answer should be. Are we doing something wrong