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valentina_108 [34]

4 years ago

10

Help please this problem thank you

1 answer:

tangare [24]4 years ago

8 0

The value of x is 25.

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A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich

Bess [88]

Answer:

a). k = 2.0794

b). $A_{t}=A_{0}(2^{3t} )$

c). 13107200 cells

d). rate of growth after 6 hours = 27255112

e). 4.76 hours

Step-by-step explanation:

From the formula of bacterial population,

$A_{t}=A_{0}e^{kt}$

Where $A_{t}$ = Bacterial population after time t

$A_{0}$ = Initial population

k = relative growth factor

t = duration or time

a). For $A_{t}=2\times 50=100$ cells

and $A_{0}=50$ cells

Time t = 20 minutes = $\frac{1}{3}$ hours

Now we plug in these values in the formula,

100 = $50(e^{\frac{k}{3}})$

$e^{\frac{k}{3}}=2$

By taking natural log on both the sides of the equation,

$\frac{k}{3}(lne)=ln(2)$

k = 3ln(2) = 2.0794

b). To get the expression we will plug in the value of k in the formula.

$A_{t}=A_{0}e^{kt}$

Since k = 3ln(2)

$A_{t}=A_{0}e^{3t(ln2)}$

Let y = $e^{3t(ln2)}$

By taking natural log on both the sides of the equation,

lny = $ln(e^{3t(ln2)} )$

lny = 3t(ln2)ln(e)

ln(y) = 3t(ln2)

ln(y) = $ln(2)^{3t}$

y = $2^{3t}$

Now our expression will be $A_{t}=A_{0}(2^{3t} )$

c). Number of cells after t = 6 hours

$A_{6}=50(2^{3\times 6} )$

$A_{6}=50(2^{18})$

$A_{6}=50\times (262144)=13107200$

d). We can get the rate of growth by finding derivative of the expression

$\frac{d}{dt}(A_{t})=\frac{d}{dt}[A_{0}(e^{kt}})]$

= $A_{0}[ke^{kt}]$

Now $\frac{d}{dt}(A_{6})=k.A_{6}$

= 2.0794×13107200

= 27255112

e) From the given formula,

$A_{t}=A_{0}(2^{3t} )$

$1000000=50(2^{3t} )$

$2^{3t}=20000$

3t(ln2) = ln(20000)

t = $\frac{ln(20000)}{3(ln2)}$

t = $\frac{9.90349}{2.07944}=4.76$ hours

3 0

3 years ago

Explain your answer to each question.

katovenus [111]

A) 3/7 is greater because 2 divided by 5 is .40 and 3 divided by 7 is .42 rounded

b) 3/10 = .3, 2/5 = .4, 14/30 = about .46, 1/2 =.5, and 8/15 = about .53

hope this helps :)

7 0

4 years ago

How do you write 309017 in word form

lara [203]

Word form:

three hundred nine thousand, seventeen

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4 years ago

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What is the answer to this

guapka [62]

Alright, first blank one is 1/3, then 2/3, then 1, then 1 1/3, then 1 2/3.
Now, shade the 1/3 and 2/3 in blue. Shade the 0, 1 and 2 in red.
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Glad I could help, and good luck!

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3 years ago

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If 2 - 2 is a factor of 2.? - bx - 10, what is the value of b?

aleksandr82 [10.1K]

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3 years ago