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2 years ago

Which one is greater 4.159 or 4.152????.

Mathematics

2 answers:

Illusion [34]2 years ago

6 0

The first option is greater.

nalin [4]2 years ago

6 0

The first option is correct:)

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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

2 years ago

1. Write a ratio and a percent for the shaded area. (1 point)

Kipish [7]

Answer:

3/10, 30%

Step-by-step explanation:

the shaded region is 9/30 which is equivilent to 3/10 and 3/10is 30 percent.

hope this helps!

8 0

3 years ago

The weights of bags of ready-to-eat salad are normally distributed with a mean of 300 grams and a standard deviation of 9 grams.

mestny [16]

Answer: 2.5% of the bags weigh less than 282 grams.

Step-by-step explanation: Just took the test and this was the correct answer! :)

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3 years ago

at the drive in it cost 5 dollars per vehicle plus 2 dollars per person in the vehicle construct an equations from this informat

Mekhanik [1.2K]

Answer:

5v+2d

Step-by-step explanation:

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3 years ago

WILL GIVE BRAINLLEST

kumpel [21]

7idjdjdbrhzuzhhwbscjcjc

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3 years ago