rachelmaddie
Full Member
- Joined
- Aug 30, 2019
- Messages
- 851
Hi. I need my work checked please.
Let the relative brightness be given by ‘b’ and stellar magnitude by ‘m’
The magnitude of relative brightness as the magnitude of stellar increases.
From the table, the ratio for any two consecutive values of ‘b’ is the same and equal to 0.4.
40/100 = 16/40 = 6.3/16 = 2.5/6.3 = 1/2.5 = 0.4
We know for the common ratio ‘r’ of a given series, the series is called a geometric sequence.
The nth term of a geometric series is given:
an = a1r^n - 1
In the given table,
m = n,b = an,r = 0.4, a1 = 100
Therefore, the equation that gives the relative brightness in terms of stellar magnitude is given as:
b = 100(0.4)^m - 1.
a
b = 100(0.4)^m - 1
Given: The stellar magnitude is, m = 9
The equation to find relative brightness is b = 100(0.4)^m - 1
Substitute 9 for ‘m’ and solve for ‘b’.
This gives,
b = 100(0.4)^9 - 1
b = 0.07
Therefore, the relative brightness for a stellar magnitude of 9 is 0.07.
b
The relative brightness for a stellar magnitude of 9 is 0.07.
Let the relative brightness be given by ‘b’ and stellar magnitude by ‘m’
The magnitude of relative brightness as the magnitude of stellar increases.
From the table, the ratio for any two consecutive values of ‘b’ is the same and equal to 0.4.
40/100 = 16/40 = 6.3/16 = 2.5/6.3 = 1/2.5 = 0.4
We know for the common ratio ‘r’ of a given series, the series is called a geometric sequence.
The nth term of a geometric series is given:
an = a1r^n - 1
In the given table,
m = n,b = an,r = 0.4, a1 = 100
Therefore, the equation that gives the relative brightness in terms of stellar magnitude is given as:
b = 100(0.4)^m - 1.
a
b = 100(0.4)^m - 1
Given: The stellar magnitude is, m = 9
The equation to find relative brightness is b = 100(0.4)^m - 1
Substitute 9 for ‘m’ and solve for ‘b’.
This gives,
b = 100(0.4)^9 - 1
b = 0.07
Therefore, the relative brightness for a stellar magnitude of 9 is 0.07.
b
The relative brightness for a stellar magnitude of 9 is 0.07.