Hivaclibtibcharkwa
𝗕𝗶𝗼𝗹𝗼𝗴𝘆 𝗧𝘂𝘁𝗼𝗿
- Joined
- Jan 17, 2021
- Messages
- 1,848
- Gender
- Male
- HSC
- 2021
-
Looking for HSC notes and resources? Check out our Notes & Resources page
How would you solve this (1 Viewer)
- Thread starter Hivaclibtibcharkwa
- Start date
So you would end up with geometric series = num_minutes_in_a_year, where n= num_times_finger_snapped. There is no way to solve this numerically so you will need to use inspection
The official solution is as follows:
This question also requires a knowledge of logarithms. Don’t stress if you don’t understand it yet!
To solve a problem like this, it is often helpful to draw a diagram and/or table to illustrate what is happening. It then becomes easier to spot a pattern. We will draw a table to compare the number of finger snaps (n) with the total time elapsed in minutes (t):
Can we find some mathematical expression that will give us the time elapsed for a certain number of finger snaps? Since the time elapsed between finger snaps always doubles, we would expect powers of 2 to be involved in the expression. In fact, we notice that the numbers in the time elapsed column are all 1 less than a power of 2. We could try the expression
but this doesn’t quite work. With a little bit of thought, you should realise that
is the correct expression. Since we can now calculate the time elapsed for any given number of finger snaps, we can work out how many finger snaps fit into a year. We do this by first finding the number of minutes in a year.
We could of course look this up on the internet; but we really should be able to work it out for ourselves! One year is 365 days, which is 365 × 24 hours, i.e. 8760 hours. This in turn is 8760 × 60 minutes; so there are 525600 minutes in a year.
Now we ask the question: for which value of n (for how many finger snaps) do we get a value of t that is close to the number of minutes in a year? In other words, we want to solve
, which gives
)
}{\:\log _{10}\left(2\right)}+1)
Since we can only have a whole number of finger snaps, we have shown that by following the pattern, we would only snap our fingers 20 times in one year.
I hope this helps!
This question also requires a knowledge of logarithms. Don’t stress if you don’t understand it yet!
To solve a problem like this, it is often helpful to draw a diagram and/or table to illustrate what is happening. It then becomes easier to spot a pattern. We will draw a table to compare the number of finger snaps (n) with the total time elapsed in minutes (t):
Can we find some mathematical expression that will give us the time elapsed for a certain number of finger snaps? Since the time elapsed between finger snaps always doubles, we would expect powers of 2 to be involved in the expression. In fact, we notice that the numbers in the time elapsed column are all 1 less than a power of 2. We could try the expression
We could of course look this up on the internet; but we really should be able to work it out for ourselves! One year is 365 days, which is 365 × 24 hours, i.e. 8760 hours. This in turn is 8760 × 60 minutes; so there are 525600 minutes in a year.
Now we ask the question: for which value of n (for how many finger snaps) do we get a value of t that is close to the number of minutes in a year? In other words, we want to solve
Since we can only have a whole number of finger snaps, we have shown that by following the pattern, we would only snap our fingers 20 times in one year.
I hope this helps!
- Joined
- Feb 26, 2008
- Messages
- 5,247
- Gender
- Male
- HSC
- 2011
This one is a similar problem: https://www.gocomics.com/foxtrot/2006/09/10