Question

Three disease-carrying organisms decay exponentially in seawater according to the following model: $$ p(t)=A e^{-1.5 t}+B e^{-0.3 t}+C e^{-0.05 t} $$ Estimate the initial concentration of each organism ( $A, B$, and $C$ ) given the following measurements: $$ \begin{array}{lccccccccc} \hline \boldsymbol{t} & 0.5 & 1 & 2 & 3 & 4 & 5 & 0 & 7 & 9 \\ \boldsymbol{p}(\boldsymbol{t}) & 0 & 4.4 & 3.2 & 2.7 & 2 & 1.9 & 1.7 & 1.4 & 1.1 \\ \hline \end{array} $$

   Three disease-carrying organisms decay exponentially in seawater according to the following model:

$$
p(t)=A e^{-1.5 t}+B e^{-0.3 t}+C e^{-0.05 t}
$$


Estimate the initial concentration of each organism ( $A, B$, and $C$ ) given the following measurements:
$$
\begin{array}{lccccccccc}
\hline \boldsymbol{t} & 0.5 & 1 & 2 & 3 & 4 & 5 & 0 & 7 & 9 \\
\boldsymbol{p}(\boldsymbol{t}) & 0 & 4.4 & 3.2 & 2.7 & 2 & 1.9 & 1.7 & 1.4 & 1.1 \\
\hline
\end{array}
$$

Applied Numerical Methods With MATLAB: for Engineers & Scientists

Steven Chapra 3rd Edition

Chapter 15, Problem 10

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We have a model for the decay of three disease-carrying organisms: $$p(t) = Ae^{-1.5t} + Be^{-0.3t} + Ce^{-0.05t}$$ We need to estimate the initial concentrations A, B, and C based on the given measurements. The initial concentrations represent the values at t = Show more…

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Three disease-carrying organisms decay exponentially in seawater according to the following model: $$ p(t)=A e^{-1.5 t}+B e^{-0.3 t}+C e^{-0.05 t} $$ Estimate the initial concentration of each organism ( $A, B$, and $C$ ) given the following measurements: $$ \begin{array}{lccccccccc} \hline \boldsymbol{t} & 0.5 & 1 & 2 & 3 & 4 & 5 & 0 & 7 & 9 \\ \boldsymbol{p}(\boldsymbol{t}) & 0 & 4.4 & 3.2 & 2.7 & 2 & 1.9 & 1.7 & 1.4 & 1.1 \\ \hline \end{array} $$

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