Question 1034815
a) find the value for k and write an exponential growth function that estimates the mass M of the bacteria colony t hours after 8 AM Monday.
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{{{M=p*e^(kt)}}}  p=5 grams, t is time in hours, k is a constant.


{{{ln(M)=ln(p)+ln(e^(kt))}}}

{{{ln(M)=ln(p)+kt*1}}}

{{{kt+ln(p)=ln(M)}}}

{{{kt=ln(M)-ln(p)}}}


{{{highlight_green(k=(ln(M)-ln(p))/t)}}}




Given that M=6.5, p=5, t=6,
{{{k=(1/6)(ln(6.5)-ln(5))}}}

{{{highlight(k=0.0437)}}}



Growth model may be restated as {{{M=5*e^(0.0437t)}}}.