The function f t = 40,000 2 t 790 gives the number of bacteria in a

Choice B is correct. It’s given that $t$ minutes after an initial observation, the number of bacteria in a population is $\mathrm{40,000}{\left(2\right)}^{\frac{t}{790}}$. This expression consists of the initial number of bacteria, $\mathrm{40,000}$, multiplied by the expression $2^{\frac{t}{790}}$. The time, in minutes, it takes for the number of bacteria to double is the increase in the value of $t$ that causes the expression $2^{\frac{t}{790}}$ to double. Since the base is $2$, the expression $2^{\frac{t}{790}}$ will double when the exponent increases by $1$. Since the exponent of this expression is $\frac{t}{790}$, the exponent will increase by $1$ when $t$ increases by $790$. Therefore, the time, in minutes, it takes for the number of bacteria in the population to double is $790$. 

Choice A is incorrect. This is the base of the exponent, not the time it takes for the number of bacteria in the population to double.

Choice C is incorrect. This is the number of minutes it takes for the population to double twice.

Choice D is incorrect. This is the number of bacteria that are initially observed, not the time it takes for the number of bacteria in the population to double.