Just Logarithms! 80 points!

Mathematics

2 answers:

jek_recluse [69]3 years ago

4 0

1. A) 0 (I’m not totally sure since there are two of the same thing, but with different answers.)

2. (Not sure)

3. C) 3

4. A) 6

5. A) 4

6. C) 4 (I’m pretty sure it’s 4 if it’s in the way I think it should be in to get 4.)

7. C) 4

8. A) 0

(I tried my best, I’m probably wrong, because I don’t exactly know how to do logarithms yet. Sorry if I got some wrong.)

Ira Lisetskai [31]3 years ago

4 0

Answer:

1) B

2) B

3) C

4) A

5) A

6) C

7) C

8) A

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A culture of bacteria has an initial population of 41000 bacteria and doubles every 5 hours. Using the formula P t = P 0 ⋅ 2 t d

Crazy boy [7]

Answer:

Population of bacteria in culture after 14 hours is 285541.

Step-by-step explanation:

We are given with $P_{t} =P_{0}(2)^{\frac{d}{t}}$

Here initial population is 41000 , t=5 and d=14

Plug in these values into the formula

$P_{14} =41000(2)^{\frac{14}{5} }$

Simplify

$P_{14}= 41000(2)^{2.8}$

=41000(6.9644)

=285540.5847...

To the nearest whole number is 285541.

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Find an equation in standard form of the parabola passing through these points: (0,-6),(-1,-12),(3,0)

Elan Coil [88]

One form of the equation of a parabola is
y = ax² + bx + c

The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6 (1)
a - b + c = -12 (2)
9a + 3b + c = 0 (3)

Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6 (4)
9a + 3b - 6 = 0
9a + 3b = 6 (5)

Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1

The equation is
y = -x² + 5x - 6

Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
= -[ (x - 2.5)² - 2.5²] - 6
= -(x - 2.5)² + 6.25 - 6

y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.

Answer: y = -(x - 2.5)² + 0.25