A certain isotope decays so that the amount A remaining after t years is given by:

A = A0 • e ^(-0.03t)

where A0 is the original amount of the isotope. To the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is ____ years.

Question

A certain isotope decays so that the amount A remaining after t years is given by:

A = A0 • e ^(-0.03t)

where A0 is the original amount of the isotope. To the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is ____ years.

loser66 · Answer

Where are you stuck?

anonymous · Answer

the entire thing! I dont even know how to start @Loser66

loser66 · Answer

A = 1/2 A0, solve for t. Dat sit

loser66 · Answer

$A_0$ is the original amount of the isotope, right?

loser66 · Answer

$ A $ is the new amount of the original one, and it is = a half of original one. That means $A=\dfrac{1}{2}A_0$

loser66 · Answer

Now, put them in, you have $\dfrac{1}{2}A_0=A_0e^{-0.03t}$
simplify $A_0$ and solve for t.
I let you finish the stuff.

anonymous · Answer

A=A0e^(-0.03t)