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photoshop1234 [79]
3 years ago
13

I'm studying a new bacteria that doubles in numbers every 25 minutes. If i start with 50 bacteria, how long until i have 5 milli

on of them
Mathematics
1 answer:
dimaraw [331]3 years ago
6 0

Answer:

415.63 minutes

Step-by-step explanation:

Growth can be represented by the equation A=A_0e^{rt}. We can find the rate at which it grows by using t=25 minutes and \frac{A_{0}}{A} =2 or double the amount at that time. The first step we always take is to divide A_0 by A.

[tex]\frac{A_{0}}{A}=e^{rt}\\2=e^{r(25)}

2=e^{(25)r}

To solve for r, we will take the natural log of both sides and use log rules to isolate r.

ln 2=ln e^{(25)r}\\ln 2=25r (ln e)\\\frac{ln2}{25} =r

We know lne=1 so we were able to cancel it out and divide both sides by 25.

We solve with a calculator \frac{ln2}{25} =r\\0.0277=r

We change 0.0277 into a percent by multiplying by 100 to get 2.77% as the rate.

The equation is A=A_0e^{0.0277t} .

We repeat the step above substituting A=5,000,000, A_0=50, and r=0.02777. Then solve for t.

5000000=50e^{0.0277t}\\\frac{5000000}{50} =e^{0.0277t}\\100000=e^{0.0277t}\\ln100000=lne^{0.0277t}\\ln100000=0.02777t(lne)\\\frac{ln100000}{0.0277} =t

t=415.63 minutes

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It takes most oceans about 6 hours to go from high tide to low tide.Suppose that the water level decreases at a rate of 3 feet p
juin [17]

Answer:

From the level of high tide to low tide, it's 18 feet.

Step-by-step explanation:

To find the change in water level, we multiply the rate (3 ft / hr) by the time (6 hrs), obtaining 18 ft.

The water level changes by 18 ft.

8 0
2 years ago
Andy is buying a car.
serg [7]

7/100* 6500=455

6500-455=6045

6045/12=503.75

Andy pays 503.75 a month

8 0
3 years ago
Open-Ended Question<br>*Picture*
My name is Ann [436]
We have to calculate the volume of the right rectangular prism.
lenght=4 1/2 in=(4+1/2) in=9/2 in
width=5 in
height=3 3/4 in=(3+3/4) in=15/4 in

Volume (right rectangular prism = lenght x width x height.
volume=9/2 in * 5 in * 15/4 in=675/8 in³

we calculate the volume of this little cube.
volume=side³
volume=(1/4 in )³=1/64 in³

Now, we calculate the number of small cubes are needed to fit the right rectangular pris by the rule of three.

1 small cube----------------1/64 in³
x---------------------------------675/8 in³

x=(1 small cube * 675/8 in³) / 1/64 in³=5400 small cubes.

Answer: we need 5400 small cubes to fit the right rectangular prism.
8 0
3 years ago
4th grade math help! Line plots
Alborosie
There are three 'x's on the 3/4 spot, so you know that there are three 3/4 inch buttons.

To find how long they are lined up, you add them.

3/4 + 3/4 + 3/4 = 9/4

9/4
as a mixed number is 2 1/4.

Good luck!
8 0
3 years ago
Solve the problem given below
vladimir1956 [14]

<u>Answer</u>

<em>12 in by 12 in</em>

<u>Explanation</u>

The original length = x

This makes the length of the cube made to be = x - (2×2)

                                                                               = (x - 4) in

height of the cube = 2 in

Volume of the cube = (x - 4) × (x - 4) × 2 = 128

                                 = (x² - 8x + 16) × 2 = 128

                                = 2x² - 16x + 32 = 128

                                 = 2x² - 16x + 32- 128=0

                                 = 2x² - 16x - 96 = 0

                                 = x² - 8x - 48 = 0

lets use the factor method to solve the quadrilatic equation above,

x² - 8x - 48 = 0

proctuct = -48

sum = -8

The two factors are; -12 and 8.

(x + 8)(x - 12) = 0

So the value of x are 12 and -8.  Since x is a length, it can not be negative.

∴ x = 12 in.

The original dimensions of the sheet are <em>12 in by 12 in</em>.

7 0
3 years ago
Read 2 more answers
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