t f(t) = 60,000(2)^410 The function 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?
Correct answer: 410 (parsed from the explanation — this source omits an answer key for this item)
Explanation
410 The correct answer is . It’s given that t minutes after an initial observation, the 60,000 2 41t0 number of bacteria in a population is ^ h . This expression consists of the 60,000 241t0 initial number of bacteria, , multiplied by the expression . The time it takes for the number of bacteria to double is the increase in the value of t that 241t0 241t0 causes the expression to double. Since the base of the expression is 2, 241t0 the expression will double when the exponent increases by 1. Since the exponent of the expression 241t0 is 41t0, the exponent will increase by 1 when t 410 increases by . Therefore the time, in minutes, it takes for the number of 410 bacteria in the population to double is .
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