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2 years ago

6

Will you help out with this equation please

1 answer:

Rina8888 [55]2 years ago

4 0

If that says 4v=3 and 2/3, then v =11/12

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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

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

$1000 = 300e^{24r}$

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

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

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

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

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

$r = 0.05$

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

2 years ago

ANSWER ASAP - 15 POINTS!!!!!!!1

Pie

The answer is : 20x^50

Hope this helps!

6 0

3 years ago

Read 2 more answers

Rewrite 7 − 8 using the additive inverse and display the new expression on a number line.

Katen [24]

Answer: A.)

Step-by-step explanation: if you start at 7 and take 8 away your left with a negative

A is correct purple line to 7 and red line to -1

Hope this helps

4 0

11 months ago

a crew workers paved 2/15 mile in 20 minutes. if they work at the same rate what portion of a mile will they pave in one hour?

ANEK [815]

Since 20 min is 1/3 of a mile 20 min*3=1 hour. then u multiply 2/5 by 3 to get 6/5.

6 0

3 years ago

Don’t need help with the scatter plot really I just need help finding the Correlation coefficient

aleksandr82 [10.1K]

난 아직 모르는 척 하지만 새로운 걸 할 수 있어

5 0

2 years ago