Help me solve this

Question

​Strontium-90 is a radioactive material that decays according to the function

A(t)=A0e−0.0244t,

where

A0

is the initial amount present and A is the amount present at time t​ (in years). Assume that a scientist has a sample of

500

grams of​ strontium-90.

​(a) What is the decay rate of​ strontium-90?

​(b) How much​ strontium-90 is left after

10

​years?

​(c) When will only

100

grams of​ strontium-90 be​ left?

​(d) What is the​ half-life of​ strontium-90?

Answer 1

A(t) = Aoe^-0.0244t = Ao/e^0.0244t

the decay rate is the coefficient of t: 0.0244 = 2.44% annually.

A(10) = 500e^-0.0244(10) = 500/1.2763 =about 392 grams left after 10 years

100 = 500e^-0.0244t

e^-0.0244t = 100/500 = 1/5 = 0.2

-0.0244t = ln(0.2) = -1.61

t =-1.61/-0.0244 = 65.96 years

t= 65 years and about 11 1/2 months

t= almost 66 years to decay to 100 grams

half life is when

1 = 2e^-0.0244t

e^-0.0244t = 1/2

-0.0244t = ln(.5)

t= 28.41 years to decay to half the original amount