The half-life of radium is 1690 years. If 90 grams are present now, how much will be present in 400 years?

76.38 g

Step-by-step explanation:

Below expresion can be used in calculating the remaining amount of radium

A(t)=A(0) (1/2)^(t/h)

Let A(t)=the remaining amount of radium

Let A(0)= amount of radium at the beginning= 90 grams

t= amount of time in years= 400 years

h=the half-life time= 1690 years

A(t)=A(0) (1/2)^(t/h)

If we substitute the values into the expresion we have

A(t) = 90 × (1/2)^(400/1690)

A(t)= 76.38 g

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!