Maths A level

[Limitedrichy]

Anyone could help me with this it would be much appreciated!!

 

Done this much so far

I know i need to get A and B from the each graph and they should be the same

[T.Vengeance]

I=aV^b

4.8 = a(4)^b

log₄(4.8) = log₄[a(4)^b]

log₄(4.8) = log₄(a) + log₄(4^b)

log₄(4.8) = log₄(a) + b*log₄(4)

log₄(4.8) = log₄(a) + b

 

b = log₄(4.8) - log₄(a)

b = log₄(4.8/a)

b = log₂²(4.8/a)

b = 0.5*log₂(4.8/a)

b = log₂(4.8/a)^0.5       (eq 1)

 

7.2 = a(8)^b

log₈(7.2) = log₈[a(8)^b]

log₈(7.2) = log₈(a) + b

 

b = log₈(7.2) - log₈(a)

b = log₈(7.2/a)

b = 1/3log₂(7.2/a)

b = log₂(7.2/a)^1/3       (eq2)

 

EQ1-EQ2:

 

0 = log₂(4.8/a)^0.5 - log₂(7.2/a)^1/3

log₂(7.2/a)^1/3 = log₂(4.8/a)^0.5

 

(7.2/a)^1/3 = (4.8/a)^0.5

4.8^0.5 / 7.2^1/3 = a^0.5 / a^1/3

1.135 = a^1/6

 

a = 1.135⁶

 

4.8 = a(4)^b                EQ 1

7.2 = a(8)^b                EQ 2

 

EQ2 / EQ1:

 

1.5 = (8)^b / (4)^b

 

1.5 = 2^3b / 2^2b

log₂(1.5) = log₂(2^3b / 2^2b)

log₂(1.5) = log₂(2^3b) - log₂(2^2b)

log₂(1.5) = 3b*log₂(2) - 2b*log₂(2)

log₂(1.5) = 3b - 2b

b = log₂(1.5)

 

a = 4.8/4^log₂(1.5)

[rhyseyness]

-snip-

 

Why have you used log in base 2, 4 and 8 rather than just doing it all in 10?

Seems over complicated to me.

 

Just to add also, the linear form of the equation is:

Log(I)=bLog(V)+Log(a)

(Looks the same as: y=mx+c)

As @T.Vengeance showed, you can work out the constants a and b from the other equations formed, then sub them in for the final linear form of the equation.

 

Hope this helps

[T.Vengeance]

Why have you used log in base 2, 4 and 8 rather than just doing it all in 10?

Seems over complicated to me.

 

Just to add also, the linear form of the equation is:

Log(I)=Log(a)+bLog(V)

(Looks the same as: y=mx+c)

As @T.Vengeance showed, you can work out the constants a and b from the other equations formed, then sub them in for the final linear form of the equation.

 

Hope this helps

 

Oh god, this is what happens when I solve math equations in the morning without sleeping. I just had a big face palm moment.

[Guest Philosophy]

Oh god, this is what happens when I solve math equations in the morning without sleeping. I just had a big face palm moment.

I just don't do math earlier than 9am.I tried that on my latest trig test I only got an 89 percent  Edit: I had a 109 Percent overall now I have a 102 Percent. 

[T.Vengeance]

I just don't do math earlier than 9am.I tried that on my latest trig test I only got an 89 percent  Edit: I had a 109 Percent overall now I have a 102 Percent. 

Yeah I remember when I had first period calculus. Damn that wasn't fun. Not fun at all.

[Guest Philosophy]

Yeah I remember when I had first period calculus. Damn that wasn't fun. Not fun at all.

I try my best to get math middle day seems to work out best  

[Biased Opinion]

I remember in high school for a full term I would start Monday with physics, then break, then math then more math the break and the finish the day with chemistry. It was fun and there is always time for math