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Lelu [443]
2 years ago
6

Pls answer number 5 evaluate each expression for the giving values of the variables

Mathematics
1 answer:
trasher [3.6K]2 years ago
8 0

Answer:

where the expression?

Step-by-step explanation:

so I can help u out?

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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
The diagram shows a right-angled triangle.
Marizza181 [45]

Answer:

11.9 Cm.

Have a nice day!

Step-by-step explanation:

cos = adj/hyp

cos 24°= hcm/ 13cm

13 cos 24°= h

11.88= h

11.9 cm

7 0
1 year ago
The question is the photo
Readme [11.4K]
For this question you can say:
5/9( °F - 32) = -10 °C
so now you should solve the equation:
5F/9 - 160/9 = -10 
⇒ 5F/9 = -10 + 160/9 ⇒ 5F/9 = -90/9 + 160/9 ⇒ 5F/9 = 70/9 ⇒ now you can multiply both sides of the equation by 9 so you will have:
5F = 70 ⇒ F = 14 ° F :)))
i hope this is helpful
have a nice day 
6 0
3 years ago
Find two consecutive even integers whose sum is 22
andrew11 [14]

10 & 12

x = 1st consecutive even number

x + 2 = 2nd consecutive even number  

x + x + 2 = 22

2x + 2 = 22

2x = 20

x = 10

x + 2 = 12

10 and 12 are the two consecutive even numbers



7 0
3 years ago
You are on the high school basketball team. The ball you use has a diameter of 9 inches. What is the volume of the ball? Use 3.1
nlexa [21]

Answer:

63.6

Step-by-step explanation:

5 0
2 years ago
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