Question 1130955
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 𝑄 = 𝑄0 × (1 + 𝑟)^𝑡
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{{{v=v[o](1+r)^t}}}
t years since 1854
r as a decimal fraction
{{{v[o]=285}}}for year 1854


{{{285(1+r)^148=379}}}
{{{solve}}}{{{for}}}{{{r}}}.

{{{log(1+r)=(1/148)*log((379/285))}}}

{{{log((1+r))=0.000836448}}}

{{{1+r=1.0019278}}}

{{{r=0.193}}}{{{percent}}}


model:  {{{highlight(v=285(1.0019278)^t)}}}



Predict When v=570 parts per million:

{{{(1.0019278)^t=2}}}

Take logs of both sides and find t.