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ELEN [110]
2 years ago
12

Suppose the bacteria population in a specimen increases at a rate proportional to the population at each moment. There were 100

bacteria 4 days ago and 100,000 bacteria 2 days ago. How many bacteria will there be by tomorrow
Mathematics
1 answer:
NNADVOKAT [17]2 years ago
7 0

9514 1404 393

Answer:

  about 3,160,000,000

Step-by-step explanation:

"Increases at a rate proportional to population" means the growth is exponential. It can be modeled by the equation ...

  p = ab^t

We can find 'a' and 'b' using the given data points.

  100 = ab^(-4) . . . . . . . population 4 days ago

  100,000 = ab^(-2) . . . population 2 days ago

Dividing the second equation by the first, we find ...

  1000 = b^2

  b = 1000^(1/2)

Substituting for b in the first equation, we have ...

  100 = a(1000^(1/2))^(-4) = a(1000^-2)

  100,000,000 = a

Then the population model is ...

  p = 100,000,000×1000^(t/2)

__

Tomorrow (t=1), the population will be ...

  p = 100,000,000 × 1000^(1/2) ≈ 31.6 × 100,000,000

  p ≈ 3,160,000,000 . . . . . bacteria by tomorrow

_____

<em>Additional comment</em>

We could write this as ...

  p = 10^(8+1.5t)

Then for t=1, this is p = 10^(8+1.5) = 10^0.5 × 10^9 = 3.16×10^9

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Tyrone saved 24$ of the 60 that he earned mowing lawns .what percent of his earnings did tyrone save
mezya [45]
If 24 of the 60 were saved then the percent saved is

(24/60) x 100

Let's imagine for a second that all 60 was saved, then 100% of the money would be saved. Which makes sense, because

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6 0
3 years ago
Find the center and radius of x^2 – 18x + y^2 -10y = -6. part two write x2 – 18x + y2 -10y = -6 in standard form
Aleks04 [339]

Answer:

see explanation

Step-by-step explanation:

I will begin with part two, first.

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius.

Given

x² - 18x + y² - 10y = - 6

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is

(x - 9)² + (y - 5)² = 100 ← in standard form

with centre = (9, 5 ) and r = \sqrt{100} = 10

4 0
2 years ago
The volume V (in cubic feet) of a right cylinder with a height of 3 feet and radius r (in feet) is given by V=3πr2. Solve the fo
Kitty [74]

Answer:

r=\sqrt{\frac{V}{3\pi}}\\\\r\approx 5.00\ ft

Step-by-step explanation:

-The volume of a cylinder is given by the formula:

V=3\pi r^2

#We make r the subject of the formula:

V=3\pi r^2\\\\r^2=\frac{V}{3\pi}\\\\r=\sqrt{\frac{V}{3\pi}}

#We then substitute for the stated volume and solve for r:

r=\sqrt{\frac{V}{3\pi}}, V=236\\\\\therefore r=r=\sqrt{\frac{236}{3\pi}}\\\\r=5.00404\approx\ 5.00\ ft

Hence, the cylinder's radius is approximately 5.00 ft

5 0
3 years ago
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