Question

The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

Answer 1

do you know a formula for half-life?
see https://en.wikipedia.org/wiki/Half-life#Formulas_for_half-life_in_exponential_decay

Answer 2

Idk how to actually do it

Answer 3

I would use this formula
\[ Amt= M \left(\frac{1}{2} \right)^{\frac{t}{t_0}} \]

in your problem, M is 361 kg
t0 is 32 days

Answer 4

Indeed^ and for the quetion, to find out how much would remain after 5 days, you would make 't' = 5

so

\[\huge \text{Amount} = 361(\frac{1}{2})^{\frac{5}{32}}\]

Answer 5

Sooo?? im lost

Answer 6

The equation that phi has given is exactly what the first half of the question asks, "write an exponential function for this decay"

So that would be just plugging in M and t_o into the equation for half life

\[\large \text{Amount} = 361(\frac{1}{2})^\frac{t}{32}\]

This would be the general equation,

Now to find the amount after 5 days, you plug in 5 for 't'

\[\large \text{Amount} = 361(\frac{1}{2})^\frac{5}{32}\]

Now you just plug that into a calculator and solve

Answer 7

28.203125 ?

Answer 8

Or is that completely wrong ?

Answer 9

Completely wrong, but that's alright, probably just missed a parenthesis

361(1/2)^(5/32) is what you would plug into a calculator

Answer 10

@$w3G_Godd

Answer 11

is the question multiple choice

Answer 12

because i remember having this question but it was multiple choice

Answer 13

Yeah but they are going to take me forever to type them

Answer 14

i still have where i did it what does your letter B say

Answer 15

the answer is here
http://www.wolframalpha.com/input/?i=361*%28.5%29^%285%2F32%29

Answer 16

\[\huge 323.945\]

Answer 17

Oh okay thanks :)

Answer 18

Its number 3 on here D:

Answer 19

but ya lol hes right