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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:

<em>Option C; 3x - y = -27 and x + 2y = 16</em>

Step-by-step explanation:

1. Let us consider the equation 21x - y = 9. In this case it would be best to keep the equation in this form, in order to find the x and y intercept. Let us first find to y - intercept, for the simplicity ⇒ 21 * ( 0 ) - y = 9 ⇒ y = - 9 when x = 0. Now if we take a look at the first plot of line q, we can see that the x value is -9 rather than the y value, so this equation doesn't match that of line q. This would eliminate the first two options being a possibility.

2. Now let us consider the equation 3x - y = -27. Let us consider the x-intercept in this case. That being said, ⇒ 3x - ( 0 ) = -27 ⇒ 3x = -27 ⇒ x = -9 when y = 0. As we can see, this coordinate matches with one of the coordinates of line q, which might mean that the second equation could match with the equation for line v.

3. To see whether Option 3 is applicable, we must take a look at the 2nd equation x + 2y = 16. Let us calculate the y - intercept here: ( 0 ) + 2y = 16 ⇒ 2y = 16 ⇒ y = 8 when x = 0. Here we can see that this coordinate matches with that of the second coordinate provided as one of the points in line v. That means that ~ <em>Answer: Option C</em>

<em />

6 0
3 years ago
Describe and correct the error in finding DC
sleet_krkn [62]

Answer:

DC = 2

Step-by-step explanation:

The wrong equation was used.

The right equation to use based on the midsegment theorem of a trapezoid is:

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MN = 8

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Substitute

8 = ½(14 + DC)

Multiply both sides by 2

8*2 = ½(14 + DC)*2

2*8 = 14 + DC

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Step-by-step explanation:

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8 0
2 years ago
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Jet001 [13]

Answer:

x=3,y=1

Step-by-step explanation:

2^x+y=16,3^x-y=9

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