The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial area of 64.6mm^2 and an observed doubling time of 4 minutes. (a)Let t be the time (in minutes) passed, and let y be the area of the sample at time t. Write a formula relating y to t. Use exact expressions to fill in the missing parts of the formula. (b)What will the area of the sample be in 18 minutes? Do not round any intermediate computations, and round your answer to the nearest tenth.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial area of 64.6mm^2 and an observed doubling time of 4 minutes.
(a)Let t be the time (in minutes) passed, and let y be the area of the sample at time t. Write a formula relating y to t. Use exact expressions to fill in the missing parts of the formula.
(b)What will the area of the sample be in 18 minutes?
Do not round any intermediate computations, and round your answer to the nearest tenth.
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