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2 years ago

Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Mathematics

1 answer:

photoshop1234 [79]2 years ago

8 0

Answer:

read the comments i cant help you yet but if you read the comments and do what they say then i can help you

Step-by-step explanation:

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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

Tom has 2 1/2 times as many cards as Harry. Together they have 98 cards. How many cards do they each have?

USPshnik [31]

Answer:

Tom has 70 cards, and Harry has 28 cards.

Step-by-step explanation:

Let h = number of cards Harry has.

Then the number of cards Tom has is 2 1/2 * h = 2.5h.

Together they have 2.5h + h = 3.5h number of cards.

Together they have 98 cards.

3.5h = 98

h = 98/3.5

h = 28

Harry has 28 cards.

Tom has 2.5h = 2.5 * 28 = 70

Answer: Tom has 70 cards, and Harry has 28 cards.

7 0

2 years ago

Help mayyy pleaseee and tyy

Kay [80]

Answer:

2x=-7y not sure tho just guessping probably wrong sorry

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Graph the equation on the coordinate plane.y=2x-1

Yakvenalex [24]

This equation is written in slope intercept form

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case:

slope (m) is 2

y-intercept (b) is (0, - 1)

To plot this on a coordinate plane plot the y-intercept (0, -1).

To graph the rest of the line you can use what you know about the slope. Rise up two units and over to the right one unit from the y-intercept. You should arrive at the point (1, 1)

Then, again from the y-intercept, go down two units and to the left one unit. You should arrive at the point (-1, -3)

Now draw a straight line through the y-intercept and the other two points you just found

The image of the graph is shown below

Hope this helped!

~Just a girl in love with Shawn Mendes

4 0

3 years ago

7.7.33

GenaCL600 [577]

We know that

At sea level, the height is 0 and
the pressure is 98 kilopascals

At 1000 ft, the height is 1000 and
the pressure <span>decreases about 11.41%

</span>i(100%-11.41%)/100----> (0.8859)

therefore
1) at 1000 ft--------> the pressure is 98*(0.8859)----------> 86.82 kilopascals
2) at 2000 ft--------> the pressure is 86.82*(0.8859)-------> 76.91 kilopascals
3) at 3000 ft--------> the pressure is 76.91*(0.8859)-------> 68.14 kilopascals
4) at 4000 ft---------> the pressure is 68.14*(0.8859)-------> 60.36 kilopascals

the answer is
<span>The pressure at an altitude of 4000 m is about </span>60.36 kilopascals

7 0

2 years ago