ter 5 Assignment $$ 1

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ter 5 Assignment $$ 1<\begin{array}{l}	ext { A sample of bacteria taken from a river has an initial concentration of } 2.5 	ext { million bacteria per milliliter and its concentration triples each week. } \ 	ext { (a) Find an exponential model that calculates the concentration (in millions) after } x 	ext { weeks. } \ 	ext { (b) Estimate the concentration (in millions) after } 1.9 	ext { weeks. } \ 	ext { Points: } 0 	ext { of } 1\end{array} $$ $$ \begin{array}{l}	ext { (a) } \mathrm{B}(\mathrm{x})=\square \ 	ext { (Type an equation using } \mathrm{x} 	ext { as the variable.) }\end{array} $$

UpStudy AI · Accepted Answer

**Step 1. Determine the Exponential Model**

Since the bacteria tripling each week means the concentration is multiplied by $$3$$ every week, and the initial concentration (at $$x=0$$) is $$2.5$$ million bacteria per milliliter, the exponential model is

$$
B(x)=2.5\cdot3^{x}
$$

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**Step 2. Estimate the Concentration After $$1.9$$ Weeks**

To estimate the concentration after $$1.9$$ weeks, substitute $$x=1.9$$ into the model:

$$
B(1.9)=2.5 \cdot 3^{1.9}
$$

Evaluate $$3^{1.9}$$ using a calculator:

$$
3^{1.9} \approx 8.063
$$

Thus,

$$
B(1.9) \approx 2.5\cdot8.063 \approx 20.16
$$

The estimated concentration is approximately $$20.16$$ million bacteria per milliliter.

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**Final Answers**

(a) $$B(x)=2.5\cdot3^{x}$$

(b) The concentration after $$1.9$$ weeks is approximately $$20.16$$ million bacteria per milliliter.
(a) $$ B(x) = 2.5 \times 3^{x} $$ (b) After 1.9 weeks, the concentration is approximately 20.16 million bacteria per milliliter.

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