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3 years ago

Please help me

Mathematics

1 answer:

My name is Ann [436]3 years ago

5 0

Its A

(12 - 7) + 2 • (4 + 6)

= 5 + 2 . 10

= 5 + 20

= 25

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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

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

$1000 = 300e^{24r}$

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

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

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

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

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

$r = 0.05$

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

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

Wats the answer for this math or

allochka39001 [22]

The answer is D because the whole circle is 369 degrees the big arc is 202 so 360- 202 is 158 then you have an inscribed angle of 35 multiply it by two to find the arc of that so it would be 70 so subtract 158-70=88 and you can see that that section of 88 is part of an inscribed angle so divide by two to get the answer of 44

5 0

3 years ago

Luke has 48 books. He puts 7 books in a box. How many boxes can he fill? Explain how you interpreted the remainder

Damm [24]

He can fill 6 boxes. 48 / 7 = 6R6.

I interpreted the remainder by removing the remainder to get the answer.

3 0

3 years ago

Read 2 more answers

What is 4/5 of 15. Pls tell MAEEE!!!

kirill115 [55]

Answer:

Step-by-step explanation:

of is a another word for multiplying or multiplication

6 0

3 years ago

What's the difference between partial variation and direct variation

shepuryov [24]

Answer:

Direct Variation is a relation that is of the form y = mx.

and

Partial Variation is a relation that is of the form y=mx+b

Explanation:

This is a simple way to see the difference between them.

Hope This help you!

8 0

3 years ago