Radium 226 has a decay rate that satisfies the differential equation d'(t)= -.00043d(t). assume that d(0)=100.
what is d(t)?
how much is left after 100 years? (round to nearest hundredth.)
to the nearest year, what is the life half life of radium 226?

A)

B)

C) τ=2326 years

Step-by-step explanation:

A)

Consider the differential equation:

Separate variables dD and dt:

Integrate: Remember that The integral of dD/D is ln(D).

And do , so:

B)

The function we have found is a function that let us know how many of Ra is after t years, so, evaluate the function at t=100:

Which rounded is 95.8.

C) For this equation it is known that the life half life τ is equal to (1/λ), where λ is the exponential number that is multiplying to -t in the D(t) function; so for this case, λ=0.00043, and the life half life is ,

which rounded is equal to 2326 years.

3x3 = 9 and 2x2 = 4

step-by-step explanation: