The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. starting with 210 grams of a radioactive isotope, how much will be left after 5 half-lives?

6.56 g

Step-by-step explanation:

We can write the mass of radioactive isotope left after a time t by using the equation

where

is the initial amount of radioactive isotope

is the half-life

is the time

In this problem, we want to know the amount of radioactive isotope left after 5 half-lives, so after

Substituting into the equation, we have

the answer is c. 23/3

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)