How long will it take for a sample of this substance to decay to 60​% of its original​ amount?

Question

Use the exponential decay​ model,

A=A0ekt​,

to solve the following.

The​ half-life of a certain substance is

21

years.

Question: How long will it take for a sample of this substance to decay to 60​%

of its original​ amount?

Answer 1

21 years to decay to 50% of original amount

a little less than 21 to decay to 60%, rough guess maybe about 15 years or so, give or take 5 years

75% is 21/2 = 10.5 years

60% left is somewhere between 10.5 and 21 years

1/2 = e^21r

ln.5 = 21r

r = (ln.5)/21 = annual rate of decay

60/100 = e^(ln.5)/21)t solve for 2

ln.6 = (ln.5)t/21

t = 21ln.6/ln.5 = about

Answer 2

0.50 = e^21k

ln 0.50 = 21k

(ln 0.50 / 21) = k

0.60 = e^{(ln 0.50 / 21)t}

Can you solve for t and answer?