The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 250 bacteria, and the population after 10 hours is double the population after 1 hour. How many bacteria will there be after 6 hours?

The correct answer is 396.85.

Step-by-step explanation:

The number of bacteria in a culture is increasing according to the law of exponential growth.

Let A = × where A is the final count of bacteria after t time and k is the rate of increase and is the initial count of bacteria.

Given the initial population is 250 bacteria, or = 250.

The population after 10 hours say M is M = 250 ×

The population after 1 hour say N is N = 250 × .

Given M = 2× N

⇒ 250 × = 500 ×

⇒ = 2×

Taking logarithm to the base e both sides gives the value of k as

10k = ㏑ 2 + k

⇒ k = = 0.07701

Amount of bacteria present after 6 hours is 250 × = 396.85.

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