Question

A scientist is measuring the amount of radioactive material in an unknown substance. When he begins measuring, there are 12.8 grams of radioactive substance. 9 days later, there are 7.33 grams. After 14 days, there are 5.38 grams. After 30 days, there are 2.00 grams. Assuming that the decay is exponential, find the equation that determines the number of grams remaining after x days and use the equation to determine the amount of radioactive material remaining after 50 days.
A. 0.56 g
B. 0.58 g
C. 3.27 g
D. 3.33 g

Answer 1

***Assuming that the decay is exponential,***

that means assume the amount A is determined by the equation
\[ A(t) = c\ e^{d\cdot t} \]
where e stands for "euler's number"

see
http://www-history.mcs.st-and.ac.uk/HistTopics/e_10000.html
https://en.wikipedia.org/wiki/E_(mathematical_constant)

Answer 2

in the equation
\[ A(x)= c\ e^{d x} \]
x stands for the number of days that have gone by, and
c and d are constants you pick so the equation will match the data

to find them, list a table of "days" and "amount" given in the problem

day amount (grams)
0 12.8
9 7.33
14 5.38
30 2.00


now use the first set of numbers: set x=0 and the amount to 12.8
\[ A(x)= c\ e^{d x} \\ 12.8= c\ e^{d \cdot 0} \\ 12.8 =c \ e^0\]

can you solve for c ?

Answer 3

is it B ?