SOLUTION: A tortoise travelled 4096 m in week one. Each week, it travelled half as far as the previous week. In what week will the tortoise travel 4 m? Please show me using a formula or equa
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Question 696834: A tortoise travelled 4096 m in week one. Each week, it travelled half as far as the previous week. In what week will the tortoise travel 4 m? Please show me using a formula or equation. I know the answer because I used the calculator but I still want to know how to find the answer using a formula or equation.I'm in grade 7 can you explain, because the previous time i didnt understand. Help!
Found 3 solutions by stanbon, josmiceli, MathTherapy:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A tortoise travelled 4096 m in week one. Each week, it travelled half as far as the previous week. In what week will the tortoise travel 4 m? Please show me using a formula or equation. I know the answer because I used the calculator but I still want to know how to find the answer using a formula or equation.
----
Look at the pattern:
#1 term: 4096
---
#2 term: 4096(1/2) = 2048
---
#3 term: 4096(1/2)^2 = 1024
----
....
....
----
nth term: 4096(1/2)^(n-1)
------
You want to find "n" when you are told the term is 4
----
Solve: 4096(1/2)^(n-1) = 4
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Note: 4096 = 2*2*2*2*2...*2*2*2 = 2^12
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So: (2^(12))(1/2)^(n-2) = 4
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Then: (2^12))(2)^(2-n) = 4
---
2^(14-n) = 2^2
---
14-n = 2
---
n = 12
----
4 is the 12th term of the sequence.
================
Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Just to get a handle on this, i'll start
by saying
where is the distance traveled for week number
I'll say that starts at , and
adds 1 more for each week,
etc.
Notice that for any particulart week,
The value is half that of the previous week
Now let
I want the condition:
You can use a calculator depending on what
functions it has. At the most basic, you can take
log base 10 of both sides
------------
Notice that I said that week one started with
so, I must add to each week number, so
in week number 11, the tortoise travels 4 m
Answer by MathTherapy(10556) (Show Source): You can put this solution on YOUR website!
A tortoise travelled 4096 m in week one. Each week, it travelled half as far as the previous week. In what week will the tortoise travel 4 m? Please show me using a formula or equation. I know the answer because I used the calculator but I still want to know how to find the answer using a formula or equation.I'm in grade 7 can you explain, because the previous time i didnt understand. Help!
The terms represent a geometric sequence with the first term, or : 4,096, r, or common ratio: , and n: the week-number that the tortoise will travel 4 m
Geometric sequence:
Therefore, becomes:
, so:
10 = n - 1
n = 10 + 1
The tortoise will travel 4 m in week n, or week
You can USE MS Excel to check!!
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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