im Confused on what the answer is ?

Question

Tritium decays according to the following exponential model A=A0e^0.055t

what is the half life of tritium to the neatest tenth of a year?

____ Year’s

Answer 1

First of all, it appears that there's a small error in your copying. The formula should have a negative sign in the exponent: A = A_oe^-0.055t

Since whatever amount of tritium you are given is going to decay to half that amount during the half-life, you substitute 2 for A_o and 1 for A:

1 = 2e^-0.055t

Divide both sides by 2

0.5 = e^-0.055t

Now use natural logs:

ln (0.5) = ln (e^-0.055t)

Apply the power property of logs:

ln 0.5 = -0.055t ln e

ln e = 1 , so it goes away

ln 0.5 = -0.055t

Divide both sides by -0.055

ln 0.5 / -0.055 = t

12.60267601 = t

Round as instructed.

Best wishes!