The function f t = 60,000 2 t 410 gives the number of bacteria in a population t minutes after

Question

The function f t = 60,000 2 t 410 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

The correct answer is 410 . It's given that t minutes after an initial observation, the number of bacteria in a population is 60,000 2 t 410 . This expression consists of the initial number of bacteria, 60,000 , multiplied by the expression 2 t 410 . The time it takes for the number of bacteria to double is the increase in the value of t that causes the expression 2 t 410 to double. Since the base of the expression 2 t 410 is 2 , the expression 2 t 410 will double when the exponent increases by 1 . Since the exponent of the expression 2 t 410 is t 410 , the exponent will increase by 1 when t increases by 410 . Therefore the time, in minutes, it takes for the number of bacteria in the population to double is 410 .

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