Question

For the following exercise, choose the correct answer choice.

A doctor and injects a patient with 13 milligrams of radioactive dye that decays exponentially. After 12 minutes, there are 4.75 milligrams of dye remaining in the patient’s system. Which is an appropriate model for this situation?

a. f(t) = 13(0.0805)t 

b. f(t) = 13e0.9195t 

c. f(t) = 13e(−0.0839t) 

d. f(t) = 4.75/1+13e−0.83925t

Answer 1

Consider that a doctor injects a patient with 13 milligrams of radioactive dye that decays exponentially. After 12 minutes, there are 4.75 milligrams of dye remaining in the patient’s system.

Suppose that amount of the dye remaining after t minutes is,

A(t) = 13ert

 

Hence,

   4.75 = 13er(12)

er(12) = 4.75/13

         r = 1/(12)ln(4.75/13)

         r = -0.0839

 

Hence, the amount of the dye remaining after t minutes is,

A(t) = 13e-0.0839t

 

Hence, the correct option is C.

Hence, the correct option is C.