What does b indicate for y=(A^x)^b

[brandy]

^^^
what does b indicate for y=(A^x)^b
i was thinking it should be the rate of rate of change or something, idk.

 

[Elucidus]

y=(A^x)^b=(e^{\ln A \cdot x})^b=e^{b \ln A \cdot x}

So b is a part of (along with lnA) of the exponential rate of growth (or decay).

--Elucidus

 

[brandy]

so wat does b indicate for y=e^(bx)

 

[HallsofIvy]

so wat does b indicate for y=e^(bx)

What do you mean by "what does b indicate? It is a number multiplying x! It is true that, for that particular function, y'= be^(bx) so y'= by. In this particular example b is again what Euclideus said: "the exponential rate of growth (or decay)". (He said that it was part of that along with ln A in e^(b ln(A) x) so you have just replaced his "b ln(A)" with b.

 

[brandy]

its an assignment question.
you have T=A*e^(-kt)
T=temperature
t=time
and the question asks, write down the value of k as a percentage and explain what this value indicates.
i thought if i figured out what b in y=(a^x)^b was i could explain what k is.
hence why i put it here and not in the homework section.

i have been trying to figure this out and i have some complicated excel tables going and stuff. but i still couldn't get it.

 

[Edgardo]

If you change k how does this affect the curve?

 

[nirax]

you are probably required to find out the percentage decrease of temperature per unit time. this is analogus to the radioactive decay where we say "half life" which is technically the time taken for 50% decay. so in that case the percentage decrease per unit time wud be = 50/(half life).

it means that in next 1 second that percent of matrial wud decay.

i think you should now try to figure out yourself what to do next. more explanation would be spoon feeding