Hi all, I'm having a hard time figuring out how to do the last part of my homework, I would be grateful if someone could explain to me how to do this.

A cup of tea is cooling in the shade. T degrees Celsius, a spreadsheet was used to plot log e ( T ) against time, t, in minutes.

The spreadsheet calculated the line of best fit to have an equation expressed as Log e (T) = -0.045t + 4.4543

e is ~2.71 on the calculator.

1) Show that in exponential form this is equivalently written as T = e ^ (-0.045t + 4.4543).

I'm aware that using the Log law you can write that out in 1 step, but not sure how to prove it. Because going from

Log e (T) = -0.045t + 4.4543 ----> T = e ^ (-0.045t + 4.4543)

is done in 1 step.

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 ?

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.