Help me plz!!!!

Question

The​ half-life of a radioactive substance is 31.7 years.

(a) Find the exponential decay model for this substance

(b) How long will it take a sample of 400 grams to decay to 300 grams?

(c) How much of the sample of 400 grams will remain after 20 years?

A(t)=A₀ e^________ Round to the nearest thousandth

Answer 1

Let we have exponential model A = A₀e^rt.

(a) In 31.7 years A = A₀/2. So, A₀/2 = A₀e^31.7r ; r = ln(1/2)/31.7 = - 0.021866

A = A₀e^{- 0.021866t} is our model.

(b) 300 = 400e^{- 0.021866t;} t = ln(3/4)/(- 0.021) = 13.2 years

(c) A = 400e^{- 0.021866·20} = 258.306 g

Answer 2

300 = 400(0.5)^t/31.7

0.75 = 0.5^t/31.7

ln 0.75 = (t/31.7) ln 0.5

Can you solve for t and answer?

A = 400(0.5)^20.31.7

Can you calculate and answer?