1.
A half life is 8 years
"k(8)=-\\ln 2"
"k=-\\ln 2\/8"
"R=R_0(2)^{-t\/8}"
Initially "R_0=30 mg".
(i)
"R(5)=19.45mg"
(ii)
"\\ln((2)^{-t\/8})=\\ln(0.001)"
"-t\/8=\\ln (0.001)\/\\ln(2)"
"t=8(3\\ln(10)\/\\ln(2))"
"t=79.73\\ years"
2.
The population of a community will be treble for 11 years
"k(11)=\\ln 3"
"k=\\ln 3\/11"
"P=P_0(3)^{t\/11}"
i)
"2P_0=P_0(3)^{t_1\/11}"
"(3)^{t_1\/11}=2"
"t_1=11\\cdot\\dfrac{\\ln2}{\\ln3}"
"t_1=6.94years"
"1998+6.94\\approx2005"
"2005" year
ii)
Initially "P_0=2025".
"P_2=2025(3)^{14\/11}"
"P_2=8198"
The population is 8198 in the year 2012.
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