Ask question

Ask question

All categories

2 years ago

15

Bit confused need help

1 answer:

Triss [41]2 years ago

6 0

Answer:

Step-by-step explanation:

I think they want you to reffer to each column

Institution column holds -descriptive data

grants column holds -quantitative data

aplications columns holds-quatitative data

sucess rate holds -qualitative data

You might be interested in

A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

Kaylis [27]

Answer:

A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

$P(t) = 400e^{kt}$ .

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

$\frac{90}{4} = e^{4k}$ .

Taking logarithm

$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

$P(t) = 400e^{0.7783t}$ .

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

$t = \frac{\ln 75}{0.7783} \approx 5.55$ .

So, after 5.55 hours the population of bacteria will reach 30000.

6 0

2 years ago

on a 100 pt math quiz 36 points can be earned by correctly completing division problems. how many points can be earned by comple

Tresset [83]

The answer is 64( this was kinda easy)

7 0

2 years ago

Please hurry im in a timed test

Mnenie [13.5K]

Answer:

$x^2-7x+12$

Step-by-step explanation:

$(x-3)(x-4)=\\x \cdot x + x \cdot -4 +x \cdot -3 + -3 \cdot -4=\\x^2-4x-3x+12=\\x^2-7x+12$

Hope this helps!

3 0

2 years ago

5x + 1 over 2y2

Oxana [17]

Step-by-step explanation:

So for this question just substitute the value and work out. I thought it it to the power of 2 as I can't tell from the question.

4 0

2 years ago

Describe the graph of the function. y = |x + 2|

charle [14.2K]

A chart would include

x, y

-2, 0

-1, 1

0, 2

1, 3

2, 4

The graph would look like this (Image attached)

5 0

2 years ago