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Svetllana [295]
3 years ago
9

The population of a certain species of insect is given by a differentiable function P, where P(t) is the number of insects in th

e population, in millions, at time t, where t is measured in days. When the environmental conditions are right, the population increases with respect to time at a rate that is directly proportional to the population. Starting August 15, the conditions were favorable and the population began increasing. On August 20, five days later, there were an estimated 10 million insects and the population was increasing at a rate of 2 million insects per day. Which of the following is a differential equation that models this situation?
a. P=2(t−5)+10
b. dP/dt=2/5t
c. dP/dt=1/5P
d. dP/dt=5P
Mathematics
1 answer:
Alisiya [41]3 years ago
6 0

Answer:

c. dP/dt = (1/5)P

Step-by-step explanation:

Given that the rate of change of population with respect to time dP/dt is directly proportional to the population, P, we have

dP/dt ∝ P

dP/dt = kP

Given that dP/dt = 2 million insects per day and P = 10 million insects after 5 days, So,

2 = k × 10

k = 2/10

k = 1/5

So, dP/dt = kP

dP/dt = (1/5)P

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  2x² +5x -12 = 0

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2 years ago
A paper cup is a perfect cylinder that is 6.4 cm tall and 3 cm across. Find the total area of paper needed to make the cup, to t
NNADVOKAT [17]

Hey there! I'm happy to help!

We want to find how much paper we need to make the cup. So, we need to find the surface area of the cylinder, which is basically the "walls and floors" of the cup. So, this is the circle on the bottom and the surrounding stuff that goes up. There is no circular top to this cup, which will be important when finding the total area of paper.

So, first we need to find how much paper we need to make the bottom circle. The formula for the area of a circle is A=πr². This r represents the radius, or the distance from the center of the circle to the edge. We are given that the cup is 3 cm completely across, and the radius is be half of that, so the radius is 1.5 cm. Let's find the area. We will use 3.14 for π.

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Now, we need  to find the area of the walls of the cup. The wall is a rectangle that is basically wrapped around the circle. The height of the rectangle is the height of the cup and the length of the rectangle is the circumference (perimeter) of the bottom circle because the length of the rectangle wraps completely around the circle.

First, let's find the circumference of the circle. The circumference is the diameter (distance across the circle, so 3 cm) multiplied by π. We will use 3.14 for π.

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So, this means that the long side of the rectangle is 9.42 cm, and now we multiply this by the height.

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Now, we add the rectangle area and the bottom circle area.

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But, they want us to round to the nearest centimetre, so we will just say 67 square centimetres.

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Have a wonderful day!

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