There is a population of 1,000,000 bacteria in a colony. if the number of bacteria doubles every 270 hours, what will the population be in 810 hours from now?

8000000 bacteria

Step-by-step explanation:

We would apply the formula,

y = ab^t

Where

A represents the initial amount of bacteria.

t represents the doubling time.

From the information given

A = 1000000

t = 270 hours

Since after 270 hours, the population doubles, then

y = 2 × 1000000 = 2000000

Therefore

2000000 = 1000000 × b^270

2 = b^270

Raising both sides of the equation by 1/270, it becomes

2^(1/270) = b

The equation becomes

y = 1000000 × 2^(1/270) ×t

y = 1000000 × 2^(t/270)

Therefore, the population in 810 hours hours time would be

y = 1000000 × 2^(810/270)

y = 1000000 × 2^3

y = 8000000 bacteria

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