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zloy xaker [14]
3 years ago
9

Model Exponential Growth Question :A sample of bacteria is growing at a continuously compounding rate. The sample triples in 10

days Find the formula for the daily rate. Type your answer as a fraction.
Mathematics
1 answer:
Iteru [2.4K]3 years ago
8 0

Answer:

The number of bacteria B after d days is given by

B = B_0 (3)^{\frac{1}{10} d}

where B_0 is the initial number of bacteria.  

Step-by-step explanation:

The number of bacteria B in the sample triples every 10 days, this means after the first 10th day, the number of bacteria is

B = B_0 *3,

where B_0 is the initial number of bacteria in the sample.

After the 2nd 10th days, the number of bacteria is

B = (B_0 *3)*3

after the 3rd day,

B =( B_0 *3*3)*3

and so on.

Thus, the formula we get for the number of bacteria after the <em>n</em>th 10-days is

B = B_0 (3)^n

where n is is the <em>n</em>th 10-days.

Since, n is 10 days, we have

d =10n

or

n =\dfrac{1}{10}

Substituting that into B = B_0 (3)^n, we get:

\boxed{ B = B_0 (3)^{\frac{1}{10} d}}

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Theorem: A line parallel to one side of a triangle divides the other two proportionately.
Kisachek [45]

Answer:

Segment BF = 16

Step-by-step explanation:

The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately

The given theorem is the Triangle Proportionality Theorem

According to the theorem, given that segment DE is parallel to segment BC, we have;

\dfrac{AD}{BD} = \dfrac{AE}{EC}

Therefore;

BD = \dfrac{AD}{\left(\dfrac{AE}{EC} \right) }  = AD \times \dfrac{EC}{AE}

Which gives;

BD = 6 \times \dfrac{18}{12}= 9

Similarly, given that EF is parallel to AB, we get;

\dfrac{AE}{EC} = \dfrac{BF}{FC}

Therefore;

BF = FC \times \dfrac{AE}{EC}

Which gives;

BF = 24 \times \dfrac{12}{18} = 16

Therefore, the statement that can be proved using the given theorem is segment BF = 16.

8 0
3 years ago
Ry-wy=t solve for y
Greeley [361]

Answer:

y = \frac{t}{R-w}

Step-by-step explanation:

Given

Ry - wy = t ← factor out y from each term on the left side

y(R - w) = t ( divide both sides by (R - w ) )

y = \frac{t}{R-w}

3 0
3 years ago
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What’s the measure of x for the for each figure?
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Answer:

a)73

b)27

c)58

d)70

6 0
3 years ago
If $10,000 is invested at a rate of 2.5 percent for 5 years, how much money is in the account at
Rzqust [24]

Answer:

$8,750

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, first thing's first. Find 2.5% of $10,000.

$10,000*0.025=$250

$250 dollars for 5 years is $250*5=$1,250

Finally, 10,000-$1,250=$8,750

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

Please, please give brainliest, it would be greatly appreciated, I only a few more before I advance, thanks!

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4 years ago
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B is miles he went, for c at the rate he's going at he'll probably be there after five minutes that is all I know 
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