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

Question

The function f t = 40,000 2 t 790 gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

Accepted Answer

Choice B is correct. It&rsquo;s given that t minutes after an initial observation, the number of bacteria in a population is 40,000 2 t 790 . This expression consists of the initial number of bacteria, 40,000 , multiplied by the expression 2 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 t 790 to double. Since the base is 2 , the expression 2 t 790 will double when the exponent increases by 1 . Since the exponent of this expression is 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.

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