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Exercise 1.4 A distance is 3/4 lightzeit in size at time 0.44, what speed is it growing?
I think you are good with these tanh(1.5t) exercises. I should move on.
How about the inverse, you very quickly got the knack of going from time t to the distance that grows at speed c. Call that R(t).
maybe we can go back from the distance R to t
Can your calculator do the natural logarithm "ln"? If so then you can calculate the inverse of the R(t) function and go back from R --> t
If at some time t, the distances growing at speed c are R of a lightzeit, then the time is
t = ln((1+R)/(1-R))/3
I think you already found that for time t=0.8 that R=0.83, so we could check by working back from R=0.83
Does ln(1.83/0.17)/3 = 0.8?
Imagine you find yourself back in a time when distances sized 0.71 lightzeit are growing at speed c.
Has the Earth formed yet? If it has, are there single-celled living organisms?
I'm hesitant about presenting the formula for the size of a generic distance growing over time, because of the 2/3 power. Does your calculator do sinh(1.5t)^(2/3)?
I think you are good with these tanh(1.5t) exercises. I should move on.
How about the inverse, you very quickly got the knack of going from time t to the distance that grows at speed c. Call that R(t).
maybe we can go back from the distance R to t
Can your calculator do the natural logarithm "ln"? If so then you can calculate the inverse of the R(t) function and go back from R --> t
If at some time t, the distances growing at speed c are R of a lightzeit, then the time is
t = ln((1+R)/(1-R))/3
I think you already found that for time t=0.8 that R=0.83, so we could check by working back from R=0.83
Does ln(1.83/0.17)/3 = 0.8?
Imagine you find yourself back in a time when distances sized 0.71 lightzeit are growing at speed c.
Has the Earth formed yet? If it has, are there single-celled living organisms?
I'm hesitant about presenting the formula for the size of a generic distance growing over time, because of the 2/3 power. Does your calculator do sinh(1.5t)^(2/3)?
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