Question 928040
given:

the half-life of radioactive plutonium-238 is {{{87.7}}} years

and starting amount {{{10gr}}}


a) Build an exponential function that models the amount of plutonium-238 after {{{t}}} years.


{{{A=A[o](0.5)^(t/87.7 )}}} ...where {{{A}}} - amount after {{{t}}} years , {{{A[o]}}} -amount started with


b) Use your function to determine the amount of plutonium-238 remaining after {{{200}}} years. Solve this algebraically.


{{{A[o]=10gr}}}
{{{t=200}}} years

{{{A=10(0.5)^((200cross(years))/(87.7cross(years)) )}}}...since exponent is not visible here, it is {{{(200cross(years))/(87.7cross(years))=2.280501710376283 }}}


{{{A=10gr(0.5)^(2.280501710376283 ) }}}

{{{A=10gr(0.205826)}}}

{{{A=2.05826gr}}}