QuestionA sample of bacteria taken from a river has an initial concentration of 3 million bacteria per milliliter and its concentration doubles each week. (a) Find an exponential model that calculates the concentration (in millions) after x weeks. (b) Estimate the concentration (in millions) after 1.7 weeks. (a) $B(x)=$ $\square$ (Type an equation using $x$ as the variable.)

Studdy Solution
Use the model to estimate the concentration after 1.7 weeks.
Substitute $x = 1.7$ into the model:
$$B(1.7) = 3 \cdot 2^{1.7}$$
Calculate $2^{1.7}$ using a calculator:
$$2^{1.7} \approx 3.249$$
Now multiply by 3:
$$B(1.7) \approx 3 \cdot 3.249 \approx 9.747$$
The estimated concentration after 1.7 weeks is approximately 9.747 million bacteria per milliliter.