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The zebra mussel, Dreissena polymorpha, filters particulate organic carbon
(POC) from water as part of its feeding pattern. The concentration,
c, of
POC (in milligrams per liter) remaining in a particular bay
m months after the introduction of a population of zebra mussels can be estimated using the following equation.

c=0.4*0.9^(m)
According to this estimate, how many milligrams per liter of
POC were in the bay when the zebra mussels were first introduced?

The zebra mussel, Dreissena polymorpha, filters particulate organic carbon $(P O C)$ from water as part of its feeding pattern. The concentration, $c$ , of $P O C$ (in milligrams per liter) remaining in a particular bay $m$ months after the introduction of a population of zebra mussels can be estimated using the following equation. $\newline$ $c=0.4 \cdot 0.9^{m}$ $\newline$ According to this estimate, how many milligrams per liter of $P O C$ were in the bay when the zebra mussels were first introduced?

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Write exponential functions: word problems

Full solution

Q. The zebra mussel, Dreissena polymorpha, filters particulate organic carbon

(P O C)

from water as part of its feeding pattern. The concentration,

c

, of

P O C

(in milligrams per liter) remaining in a particular bay

m

months after the introduction of a population of zebra mussels can be estimated using the following equation.

\newline

c=0.4 \cdot 0.9^{m}

\newline

According to this estimate, how many milligrams per liter of

P O C

were in the bay when the zebra mussels were first introduced?

Identify initial condition: Identify the initial condition for the concentration of POC. To find the initial concentration of POC when the zebra mussels were first introduced, we need to evaluate the given equation at the start time, which is when $m = 0$ months.
Substitute $m=0$ : Substitute $m = 0$ into the equation to find the initial concentration. $\newline$ Using the equation $c = 0.4 \times 0.9^{m}$ , we substitute $m$ with $0$ to find the initial concentration. $\newline$ $c = 0.4 \times 0.9^{0}$
Calculate $0.9^0$ : Calculate the value of $0.9$ raised to the power of $0$ . $\newline$ Any non-zero number raised to the power of $0$ is $1$ . $\newline$ $0.9^{0} = 1$
Multiply $0$ . $4$ : Multiply $0.4$ by $1$ to find the initial concentration of POC. $\newline$ $c = 0.4 \times 1$ $\newline$ $c = 0.4$

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