Please I need the answer to this, it would be greatly appreciated.

Question

A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 21 minutes. At the start of the experiment, 34.7g is present.

(a) Let t

 be the time (in minutes) since the start of the experiment, and let y

 be the amount of the substance at time t. Write a formula relating y to t.

Use exact expressions to fill in the missing parts of the formula. Do not use approximations.

(b) How much will be present in 13 minutes?

Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

a) The equation you will use is P=Poe^(-kt) as the base.

Simply replace the P variable with 'y' thus written as y= yo*e^(-kt).

First, you need to find the value of 'k' (the constant), so you will use the half-life value given to help with that calculation.

We will plug the half-life value (21, y0/2) into the y= yo*e(-kt).

y becomes yo/2, where yo is the initial value of the material, as it is half at exactly 21 minutes.

yo/2 = yo * e(-k(21)) Divide yo over and take the natural log, 'Ln', on both sides.

.5 = e^(-k(21))

ln(.5) = -k(21) Divide by -21 on both sides.

k= - ln(.5)/(21)

k= .033007

y = yo *e^(-(.033007)t) Is the equation for this material's decay.

b) Now, with the equation, go ahead plugin yo= 34.7, and t= 13. In regard to the time and the amount initially given.

y = yo *e^(-(.033007)t)

= (34.7)*e^(-(.033007)(13))

= (34.7)*e^(-.429091)

= 22.5931

= 22.6 grams (rounded to the tenth)

Free to let me know if I got something off tutors! This should help you get started at least. Good Luck.