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laila [671]
2 years ago
9

Use the function m=w-4 to find the value of m=8

Mathematics
1 answer:
Alex_Xolod [135]2 years ago
6 0
Finding the value of w

We want to find the value of w that makes m = 8 in the equation:

m = w - 4

We just replace m by 8 in the equation:

m = w - 4

8 = w - 4

We add 4 both sides of the equation:

8 + 4 = w - 4 + 4

8 + 4 = w

12 = w

Then

<h2>if w = 12, then m = 8</h2>
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A researcher wants to determine the impact of soil type on the growth of a certain type of plant. She grows three plants in each
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a. The mean growth of plant is same for each type of soil.

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Can someone show me the workings out for each of these three questions
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3 years ago
A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich
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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

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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}})

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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

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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

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