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marta [7]
3 years ago
6

A bacterial culture starts with 500 bacteria and doubles in size every half-hour.

Mathematics
2 answers:
tekilochka [14]3 years ago
8 0

Answer:

a). 32000

b). T_{t}=500\times 4^{t}

c). 1259

Step-by-step explanation:

Growth of a bacteria is always exponential. Therefore, population of the bacteria is represented by the the geometric sequence.

Sum of the bacterial population after t hours will be represented by

T_{n}=ar^{n}

Where a = population at the start

r = ratio with the population is growing

n = time or duration of the growth in one hour

a). Population of 500 bacteria gets doubled after half an hour.

Or gets 4 times after an hour

This sequence will have a common ratio r = 4

and initial population a = 500

Therefore, population of the bacteria after 3 hours will be

T_{3}=500\times 4^{3}

T_{3}=32000  

b). After t hours number of bacteria will be represented by

T_{t}=500\times 4^{t}

c). We have to calculate the population after 40 minutes.

That means duration 't' = 40 minutes of \frac{2}{3} hours

By the formula,

T_{\frac{2}{3}}=500\times 4^{\frac{2}{3}}

T_{\frac{2}{3}}=1259.92 ≈ 1259

Therefore, number of bacteria after 40 minutes will be 1259.

DaniilM [7]3 years ago
3 0

Answer:

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 = 500

t = 1/2 hours

Since after 1/2 hours, the population doubles, then

y = 2 × 500 = 1000

Therefore

1000 = 500 × b^1/2

2 = b^1/2

Raising both sides of the equation by 2, it becomes

2^2 = b^1/2 × 2

b = 4

The equation becomes

y = 500 × 4^t

Therefore, the population in 3 years time would be

y = 500 × 4^3

y = 32000

b) The number of bacteria after t years is

y = 500 × 4^t

c) To determine the number of bacteria after 40 minutes, we would first convert 40 minutes to hours. It becomes

40/60 = 2/3 hours. Therefore

y = 500 × 4^2/3

y = 1259

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Answer:

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Step-by-step explanation:

Since $15.24 is 6 issues each and you need to even out the issues add $15.24+$15.24 then you would get $30.48, because its 15.24 each 6 add them both and it would be 12 issues. And the first issue $29.88 for 12 issues is  only $29.88 while the other is $30.48 so the one with 6 issues/the second cost more than the first.

60 cents more because 29.88+60=30.48.

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3 years ago
Mattie uses the discriminant to determine the number of zeros the q
enot [183]

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so given

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2 years ago
Review
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5 0
2 years ago
F(x)= 2/3x -6 what is the value of f(-9)
STALIN [3.7K]

f(-9) means x is -9

Replace x with -9 and solve:

2/3(-9) - 6

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3 0
3 years ago
From 1960 to 2010, a certain money stock measure was growing at the rate of approximately 43e(1/2)x billion dollars per decade,
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Answer:

1222 billion dollars.

Step-by-step explanation:

To find the total increase from 1960 to 2010, we need to find the growth of each decade and sum them all:

In the period 1960-1970, we have x = 1, and the growth is:

y(1) = 43e(1/2) = 70.895

In the period 1970-1980, we have x = 2, and the growth is:

y(2) = 43e(2/2) = 116.8861

The growth in the following 3 periods are:

y(3) = 43e(3/2) =192.7126

y(4) = 43e(4/2) = 317.7294

y(5) = 43e(5/2) =523.8472

So the total growth in the period 1960 - 2010 is:

Total = y(1) + y(2) + y(3) + y(4) + y(5)

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Total = 1222.08\ billion\ dollars

Rounding to the nearest billion dollars, we have a total of 1222 billion dollars.

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