sat-dog

Choice D is correct. Let $y$ represent the number of cells per milliliter $x$ hours after the initial observation. Since the number of cells per milliliter doubles every $3$ hours, the relationship between $x$ and $y$ can be represented by an exponential equation of the form $y=a{\left(b\right)}^{\frac{x}{k}}$, where $a$ is the number of cells per milliliter during the initial observation and the number of cells per milliliter increases by a factor of $b$ every $k$ hours. It’s given that there were $\mathrm{300,000}$ cells per milliliter during the initial observation. Therefore, $a=\mathrm{300,000}$. It’s also given that the number of cells per milliliter doubles, or increases by a factor of $2$, every $3$ hours. Therefore, $b=2$ and $k=3$. Substituting $\mathrm{300,000}$ for $a$, $2$ for $b$, and $3$ for $k$ in the equation $y=a{\left(b\right)}^{\frac{x}{k}}$ yields $y=\mathrm{300,000}{\left(2\right)}^{\frac{x}{3}}$. The number of cells per milliliter there will be $15$ hours after the initial observation is the value of $y$ in this equation when $x=15$. Substituting $15$ for $x$ in the equation $y=\mathrm{300,000}{\left(2\right)}^{\frac{x}{3}}$ yields $y=\mathrm{300,000}{\left(2\right)}^{\frac{15}{3}}$, or $y=\mathrm{300,000}{\left(2\right)}^5$. This is equivalent to $y=\mathrm{300,000}\left(32\right)$, or $y=\mathrm{9,600,000}$. Therefore, $15$ hours after the initial observation, there will be $\mathrm{9,600,000}$ cells per milliliter.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.