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otez555 [7]
3 years ago
7

In a lab experiment, 100 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to dou

ble every 12 hours. How long would it be, to the nearest tenth of an hour, until there are 260 bacteria present?
Mathematics
2 answers:
Hoochie [10]3 years ago
8 0

Answer:

  16.5 hours

Step-by-step explanation:

You know the initial value (100) and the growth factor (2), along with the period associated with that growth factor (12 hours). This lets you write the exponential growth equation as ...

  n = 100×2^(t/12)

For n=260, we can divide by 100 and take the log.

  260 = 100×2^(t/12)

  2.6 = 2^(t/12)

  log(2.6) = (t/12)log(2) . . . . next, divide by the coefficient of t

  12×log(2.6)/log(2) = t ≈ 16.5 . . . . hours

It will be about 16.5 hours until there are 260 bacteria present.

NikAS [45]3 years ago
5 0

Answer: 16.5 hours

Step-by-step explanation:

this is an example of exponential growth

P = initial * (rate)^x

there are 100 bacteria initially and the rate is 2 since they double, and x would be t/12, because it takes 12 hours to double

so the equation is P = 100 * 2^(t/12)

now substitute 260 in for P and solve for t

260 = 100 * 2^(t/12)

2.6 = 2^(t/12)

t/12 = log_{2}2.6

t = 12(log_{2}2.6)

t = 16.5 hours

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Answer:

#1: 751.56 mm²

#2: 477 km²

Step-by-step explanation:

First I noted the semicircle on the left, which has a radius of 12.5 mm. The formula for finding the area of a semicircle is 1/2(πr²).

1/2(3.14 * (12.5)²)

<em>12.5 squared is 156.25.</em>

1/2(3.14 * 156.25)

<em>Multiply 3.14 by 156.25 to get 490.625.</em>

1/2(490.625)

<em>Divide 490.625 by 2 to get 245.3125.</em>

245.3125 mm² for the semicircle

Then, I split the rest of into a 12.5 by 25 rectangle and a 31 by 12.5 triangle.

(12.5 * 25) + 1/2(31 * 12.5)

<em>Multiply 12.5 by 25 to get 312.5.</em>

312.5 + 1/2(31 * 12.5)

<em>Multiply 31 by 12.5 to get 387.5.</em>

312.5 + 1/2(387.5)

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312.5 + 193.75

<em>Add 312.5 and 193.75 to get 506.25.</em>

506.25 mm² for the rest of the figure.

Now add the two measures, and you have your answer for #1.

245.3125 + 506.25 = 751.5625 mm², which rounds to 751.56 mm².

The area of the composite figure is 751.56 mm².

Now for #2. First, find the area of the triangle.

1/2(40 * 27)

<em>Multiply 40 by 27 to get 1080.</em>

1/2(1080)

<em>Multiply 1/2 by 1080.</em>

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Now find the area of the circle.

3.14 * 6²

3.14 * 36

113.04 km² for the circle.

Now subtract the area of the circle from the area of the triangle.

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476.96 km², which rounds to 477.0 km².

The area of the shaded region is 477 km².

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Answer:

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