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Pavlova-9 [17]
3 years ago
15

Bacteria culture doubles every 20 minutes. After two hours there are 28800 bacteria. What was the initial amount?

Mathematics
1 answer:
wlad13 [49]3 years ago
8 0

Answer:

450 bacteria.

Step-by-step explanation:

To find this, we can set up an exponential equation as shown:

28800 = a (2)^{\frac{120}{20} }

**'a' being the initial value

** '2' representing the culture doubling

Simplify the equation down:

28800 = a (2)^{6}

28800 = 64a\\a = 450.

Therefore, the initial amount of bacteria was 450.

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shepuryov [24]

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The point-slope formula states:

(

y

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y

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x

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(

y

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1

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x

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3

)

(

y

+

1

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x

+

3

)

If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for

y

. The slope-intercept form of a linear equation is:

y

=

m

x

+

b

Where

m

is the slope and

b

is the y-intercept value.

y

+

1

=

(

3

5

⋅

x

)

+

(

3

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⋅

3

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y

+

1

=

3

5

x

+

9

5

y

+

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−

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=

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x

+

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−

1

y

+

0

=

3

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x

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9

5

−

5

5

y

=

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5

x

+

4

5

The point-slope formula states:

(

y

−

y

1

)

=

m

(

x

−

x

1

)

Where

m

is the slope and

(

x

1

y

1

)

is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

(

y

−

−

1

)

=

3

5

(

x

−

−

3

)

(

y

+

1

)

=

3

5

(

x

+

3

)

If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for

y

. The slope-intercept form of a linear equation is:

y

=

m

x

+

b

Where

m

is the slope and

b

is the y-intercept value.

y

+

1

=

(

3

5

⋅

x

)

+

(

3

5

⋅

3

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+

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=

3

5

x

+

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y

+

1

−

1

=

3

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+

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−

1

y

+

0

=

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5

x

+

9

5

−

5

5

y

=

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5

x

+

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5

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