Question

The amount of radioactive uranium changes with time. The table below shows the amount of radioactive uranium f(t) left after time t.

t(hours) 0 0.5 1
f(t) 100 50 25

Which exponential function best represents the relationship between f(t) and t?

f(t) = 100(0.25)t

f(t) = 0.25(100)t

f(t) = 100 (0.5)t

f(t) = 0.25(50)t

Answer 1

problem based on differential equation

Answer 2

what do you mean?

Answer 3

\[\frac{ dx }{ dt }=-kx\]

Answer 4

after solving the differential eqn,we get \[x=e ^{-kt}\]

Answer 5

where dx/dt is the rate of change of uranium,x represents the initial amount of U,k is the decay constant & t is the time

Answer 6

if t=0,then \[x=x_{0}\]

Answer 7

substitue these values in \[x=a.e ^{-kt}\] ,we get x=a.1

Answer 8

sorry.....we get \[x_{0}=a.1=a\]

Answer 9

so,at t=0,\[x-x _{0}=a=100\]

Answer 10

therefore,\[x=x _{0}e ^{-kt}\]

Answer 11

sorry...i've tried my best ....its tedious......really sorry