Function of equition can you please write more clearly

Question

Strontium 90 is a radioactive isotope that decays according to the eqaution , where  is the initial amount present and  is the amount present after t years. If you begin with 250 grams of strontium 90,(a) How much strontium 90 will be left after 10 years? Round your answer to the nearest tenth of a gram. grams(b) When will 125 grams of strontium 90 be left? Round your answer to the nearest tenth of a year. years

Answer 1

At = 250e^-.0244(10)

=250e^-..244

= 195.872 g after 10 years

125 = 250e^-.0244t

125/250 = e^-.0244t

take natural logs of both sides to get

ln(125/250) = -.0244t

ln(.5) = -.0244t

-.0244t = ln.5

t = ln.5/-.0244 = 28.4 years to become 125 g

Answer 2

This is exponential decay,

A(t) = A(0) exp(-rt)

r=0.0244 / year

t = time in years, 10 years

A(10) = A(0) exp(-0.244) = 0.783 A(0)

Use A(0) =250 gm to get A(10)

Next

A(t) = 125, A(0) = 250

A(t)/A(0) = 125/250 = 0.50 = exp(-0.0244 t)

t is the half-life of the element

ln(0.50) = -0.0244 t

solve for half-life

-0.693 = -0.0244 t

t = 0.693/0.0244 years

t = years