Ask question

Ask question

All categories

1 month ago

9

Model Exponential Growth Question :A sample of bacteria is growing at a continuously compounding rate. The sample triples in 10

days Find the formula for the daily rate. Type your answer as a fraction.

1 answer:

Inessa [12.5K]1 month ago

8 0

Answer:

The bacteria count $B$ after $d$ days is represented by

$B = B_0 (3)^{\frac{1}{10} d}$

where $B_0$ indicates the starting amount of bacteria.

Step-by-step explanation:

In the sample, the bacterial population triples every 10 days, which implies that at the completion of the first 10 days, the bacterial count reaches

$B = B_0 *3,$

where $B_0$ denotes the original count of bacteria in the sample.

Following the second set of 10 days, the bacterial count becomes

$B = (B_0 *3)*3$

after the third set of days,

$B =( B_0 *3*3)*3$

and this pattern continues.

This leads us to the formula for the bacterial population after the nth period of 10 days, expressed as

$B = B_0 (3)^n$

where $n$ signifies the nth 10-day segment.

Since $n$ equals 10 days, we arrive at

$d =10n$

which simplifies to

$n =\dfrac{1}{10}$

By substituting this back into $B = B_0 (3)^n$ , we find:

$\boxed{ B = B_0 (3)^{\frac{1}{10} d}}$

You might be interested in

Sanjit drives the 45 km distance between York and Leeds he then drives a further 42 km from Leeds to Blackpool

Leona [12618]

The average speed for his entire journey from York to Blackpool is about 61.41 km/h.

Here’s a breakdown of how we arrive at this:

$\text{ The average speed}=\frac{\text{Total distance covered}}{\text{Total time taken}}$

The distance he travelled from York to Leeds is 45 km,

and the speed during that section was 54 km/h.

Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).

Next, the distance from Leeds to Blackpool is 42 km,

and the time for that leg of the journey is 35 minutes, which is 35/60 hours.

This leads to the total duration for his trip as

$=\frac{45}{54}+\frac{35}{60}=\frac{450+315}{540}=\frac{765}{540}=\frac{17}{12}$ hours.

The cumulative distance covered equals 45 + 42 = 87 km.

Thus, his average speed is calculated as:

$=\frac{87}{17/12}= \frac{12\times 87}{17}=\frac{1044}{17}=61.4117647\approx 61.41\text{ km per hour}$

3 0

1 month ago

Read 2 more answers

Please help! Tim and Jane both work at a company that sells boxes of breakfast cereal. The boxes of cereal cost £3.00 and the am

PIT_PIT [12445]

Jane must lower the price by 20%

7 0

16 days ago

Suppose that the weights of airline passenger bags are normally distributed with a mean of 47.88 pounds and a standard deviation

Zina [12379]

Answer:

There is a probability of 24.51% that the weight of a bag exceeds the maximum permitted weight of 50 pounds.

Step-by-step explanation:

Problems dealing with normally distributed samples can be addressed using the z-score formula.

For a set with the mean $\mu$ and a standard deviation $\sigma$ , the z-score for a measure X is calculated by

$Z = \frac{X - \mu}{\sigma}$

Once the Z-score is determined, we consult the z-score table to find the related p-value for this score. The p-value signifies the likelihood that the measured value is less than X. Since all probabilities total 1, calculating 1 minus the p-value gives us the probability that the measure exceeds X.

For this case

Imagine the weights of passenger bags are normally distributed with a mean of 47.88 pounds and a standard deviation of 3.09 pounds, thus $\mu = 47.88, \sigma = 3.09$

What probability exists that a bag’s weight will surpass the maximum allowable of 50 pounds?

That translates to $P(X > 50)$

Thus

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{50 - 47.88}{3.09}$

$Z = 0.69$

$Z = 0.69$ has a p-value of 0.7549.

<pthis indicates="" that="" src="https://tex.z-dn.net/?f=P%28X%20%5Cleq%2050%29%20%3D%200.7549" id="TexFormula10" title="P(X \leq 50) = 0.7549" alt="P(X \leq 50) = 0.7549" align="absmiddle" class="latex-formula">.

Additionally, we have that

$P(X \leq 50) + P(X > 50) = 1$

$P(X > 50) = 1 - 0.7549 = 0.2451$

There is a probability of 24.51% that the weight of a bag will exceed the maximum allowable weight of 50 pounds.

</pthis>

6 0

1 month ago

Two thirds of a straight angle

PIT_PIT [12445]

Answer:

Two thirds of a straight angle is 120°

Explanation:

First, we define a straight angle:

A straight angle measures 180°

Now, we need to find two thirds of that straight angle

To compute the fraction, multiply the straight angle's measurement by $\frac{2}{3}$

Thus:

$\frac{2}{3}$ of a straight angle = $\frac{2}{3} * 180 = 120$ degrees

Hope this helps:)

4 0

24 days ago

How many sets of 7 questions can be chosen from a file of 25 questions?

Inessa [12570]

Response:

3

Step-by-step explanation:

25 ÷ 7 = 3.5

Since full sets are required, you simply take 3

8 0

21 day ago

Read 2 more answers