This is because it is essentialy the definition of log to the base e that:

if , then by definition of the function

You have:2) Hence write the expression in the form T=Ae ^ -0.045t

Show that A=86 to the nearest correct integer.

Do i just substitute 86 in to A ?

and by the law of exponents this means:

3)The rule for T can also be written in the form T = 86 * 2 ^ -kt

a) If T = 86 * 2 ^ -kt =

86e ^ -0.045t

Find the value of K to 3 decimals

I actually have NO IDEA how to do this one ?!

b) Hence write the time taken for the Excess temperature (The initial temperature which is 86) to be halved and show that

K = 1/H

Let H be the Time.

If anyone could help me out that would be great, I'm going to need to learn this for my up-coming test in a week. Thanks everyone.