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3 years ago

Please help it’s due at 11:59

Mathematics

1 answer:

Masteriza [31]3 years ago

6 0

Answer:

c=-16

Step-by-step explanation:

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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

What is the standard form equation of the line shown below? (1 point)

kaheart [24]

Answer:

Choice 1. -3x + 2y = 5.

Step-by-step explanation:

The slope of the line = y2-y1/x2-x1

= (4 - 1) / (1 - (-1))

= 3/2.

To find the equation of the line we use the point-slope form of the equation of a line:

y - y1 = m(x - x1) where m = slope and (x1, y1) is a point on the line. So using m = 3/2 and the point (1, 4):

y - 4 = 3/2(x - 1)

y - 4 = 3/2 x - 3/2

Multiply through by 2:

2y - 8 = 3x - 3

-3x + 2y = -3 + 8

-3x + 2y = 5 (answer).

6 0

4 years ago

What is -13 equal to

iogann1982 [59]

The answer is positive 13

8 0

3 years ago

a baseball player has already scored 56 points in a game the team record for points in a game is 72 which equation will allow yo

QveST [7]

Answer: 16

Step-by-step explanation:

72 is the record - 56 which the player has already scored = 16 points is what would be needed to tie the record

6 0

3 years ago

I’m not sure how to get the gradient

snow_tiger [21]

The gradient is 2.

You divide the increase in y (2) by the increase in x (1)

5 0

3 years ago