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mixer [17]
3 years ago
11

The National Science Organization is monitoring the continuous exponential decline of an insect species due to deforestation. Th

ey do not know exactly how many there are remaining, but the model they are using represents the minimum number remaining in the world. They are putting measures into place in order to avoid extinction which will take effect when the minimum number reaches a certain point. According to the model, the minimum number of the species remaining, in millions, is constantly decreasing at a rate of 7.9% each year. There are at least 26 million of the species in the world right now. Once the minimum population reaches 2 million, the measures will be instated which should stop the decrease and keep the minimum population at 2 million. If P represents the actual population of the insects in the world, in millions, and t represents the time in years, then which of the following systems of inequalities can be used to determine the possible number of insects in the world over time?
Mathematics
1 answer:
kakasveta [241]3 years ago
4 0

Answer:

P\geq 26e^{-0.079t}

P\geq 2

Step-by-step explanation:

We are given that there is an exponential decay.

Also, the decrease is of constant rate 7.9% i.e. 0.079 each year.

Since, the initial amount of the species is atleast 26 million.

Thus, the inequality for the corresponding model will be, P\geq 26e^{-0.079t},

where t is the time period for the decay and P is the population.

Moreover, is is given that the population cannot be less than 2 million.

So, we get, P\geq 2.

Hence, the inequalities to determine the possible number of insects over time are given by,

P\geq 26e^{-0.079t}

P\geq 2.

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Hello, Brainly community!
ioda

Answer:

(B)  \displaystyle \frac{W(3.1) - W(2.9)}{0.2}

General Formulas and Concepts:

<u>Calculus</u>

Limits

Derivatives

  • The definition of a derivative is the slope of the tangent line.

Derivative Notation

Instantaneous Rates

  • Tangent Line: \displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}

Step-by-step explanation:

Since we are trying to find a <em>rate</em> at which W(t) changes, we must find the <em>derivative</em> at <em>t</em> = 3.

We are given 2 close answer choices that would have the same <em>numerical</em> answer but different <em>meanings</em>:

  1. (A)  \displaystyle  \lim_{t \to 3} W(t)
  2. (B)  \displaystyle \frac{W(3.1) - W(2.9)}{0.2}

If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the <em>rate</em> at which the volume would be changing and it is not a derivative.

If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a <em>derivative</em> at <em>t</em> = 3, and a derivative tells us what <em>rate</em> something is changing.

∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when <em>t</em> = 3.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

8 0
3 years ago
Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gallon and the second gas
Paraphin [41]

Answer:  3.50x + 4.00y ≤ 45

                0 < y < 11.25

<u>Step-by-step explanation:</u>

3.50x + 4.00y \leq 45\\\\\\\text{Subtract 3.50x from both sides:}\\4.00y\leq -3.50x+45\\\\\\\text{Divide everything by 4.00 (to isolate y):}\\\dfrac{4.00y}{4.00}\leq \dfrac{-3.50x}{4.00}+\dfrac{45}{4.00}\\\\\\y\leq-0.875x+11.25\\\\\\\text{Both x and y must be greater than zero, so:}\\0

8 0
3 years ago
Read 2 more answers
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konstantin123 [22]
if you start at the point (0,1), you are going to go up and over to (-2,4), which means you will go up 3 and to the left, which means negative, 2
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4 0
3 years ago
A bacteria has a doubling period of 5 days. If there are 2350 bacteria present now, how many will there be in 22 days?
topjm [15]
First abswer is 51700
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6 0
3 years ago
Find the substitution 2x+3y=-5 and y=-x+5
tatuchka [14]

Answer: x = 20, y = -15

Step-by-step explanation:

Since we already know that y=-x+5, we can just substitute in that value of y into the other equation:

2x+3y=-5\\2x+3(-x+5)=-5\\2x-3x+15=-5\\-x=-5-15\\-x=-20\\x=20

with the value of x, we can find the value of y:

y=-x+5=-20+5=-15

3 0
2 years ago
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