Two consecutive integers have sum of 137

During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

So

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

3 years ago

A flash disk has the capacity of storing 1 megabyte of data. How many kilobytes of data can be stored in the same flash disk

Luden [163]

For this sort of problem, you need to be familiar with prefixes.

So:

megabyte = $1 *10^6$ bytes

kilobyte = $1*10^3$ bytes

and a regular byte would just be $1$

Now, you will need to do a conversion:

$1megabyte*\frac{1*10^6bytes}{1megabyte}*\frac{1*10^{-3}kilobyte}{1byte}$

I'm going to explain this just in case, but we convert megabytes to regular bytes in the first half by using the information I gave you above. (In one megabyte, there are $1*10^6$ bytes!)

In the second fraction thought, remember one kilobyte is $1*10^3$ bytes. However, you usually only see one of each thing on the bottom of fractions, so you need to add a negative sign to the 3. (technically you could just do $\frac{1kilobyte}{1*10^3bytes}$ , but I think it is more correct to do write it out how I did).

*** They do equal the same thing though! Do whichever way is easier for you!

Now, your answer should be:

$10^3$ kilobytes (1000 kilobytes)

Hope this helped!

6 0

3 years ago

Help ASAP i need help

Reptile [31]

Answer:

Isosceles Right Triangle

Step-by-step explanation:

We look at the sides first. Two sides are equal, which means that the triangle is isosceles (equilateral means three equal sides, and scalene means no sides equal). Then we look at the only angle indicated, which is the right angle. Thus, we come to the conclusion that the triangle is an Isosceles Right Triangle.

3 0

3 years ago

PLEASE HELP

Nikolay [14]

Answer:

204,160,000

Step-by-step explanation:

Assuming the sample is a good representation of the people from the United States.

Since there were 1,000 surveyed... and 638 of them were wearing glasses, that makes a proportion of 638 out of 1,000 people, or 63,8 / 100 people... so 63.8%... or 0.638

So, if we assume that the US population is of 320 million, how many people does that make wearing glasses.... we just have to multiply 320M by 0.638

G = 320,000,000 * 0.638 = 204,160,000

8 0

3 years ago

Read 2 more answers

A number greater than 1000 whose prime factorization contains 1 prime number that does not repeat,1 prime number that repeats 3

olasank [31]

Heheheyyeyyehehhwjjwjwjjwhwhhw

8 0

3 years ago