Question

If the decay of 742 mg of an isotope is described by the function A(t)= 742e-0.03t, where t is time in years. Find the amount left after 84 years. Round your answer to the nearest mg. 

Answer 1

57.701 mg before rounding

Answer 2

Answer:

The amount left after 84 years is 59.70 mg.                        

Step-by-step explanation:

Given : If the decay of 742 mg of an isotope is described by the function $A(t)= 742e^{-0.03t}$, where t is time in years.

To find : The amount left after 84 years?

Solution :

The function of decay of 742 mg of an isotope is given by,

$A(t)= 742e^{-0.03t}$

We have to find the amount left after 84 years.

i.e. put t=84 in the given function,

$A(84)= 742e^{-0.03\times 84}$

$A(84)= 742e^{-2.52}$

$A(84)= 59.701$

Therefore, The amount left after 84 years is 59.70 mg.