At the beginning of an experiment, a scientist has 132 grams of radioactive goo. After 135 minutes, her sample has decayed to 8.25 grams.

what is the half-life of the goo in minutes?

find a formula for G(t), the amount of goo remaining at time t. G(t)=

how many grams of goo will remain after 47 minutes

Step-by-step explanation:

Based on the given numbers, we know the decay factor is ...

  8.25/132 = 1/16

in 135 minutes. We recognize 1/16 = (1/2)^4, so is 4 half-lives.

a) The half-life of goo is (135 min)/4 = 33.75 minutes

__

b) A formula for the amount remaining could be ...

  G(t) = 135(1/2)^(t/33.75)

__

c) After 47 minutes, the amount remaining is ...

  G(47) = 135(1/2)^(47/33.75) ≈ 51.42 . . . grams

Comment on the solution

The general form of a decay equation can be ...

  g(t) = (initial value)(decay factor)^(t/(decay time for the given factor))

For our G(t), we used a decay factor of 1/2 and the half-life time of 33.75 minutes.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1