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maxonik [38]
3 years ago
11

A researcher is studying a mouse population in a field. For the first year of her study, she notices that the mouse population d

emonstrates exponential growth. However, by the third year of her study, the mouse population has stabilized at approximately 500 mice (although this number fluctuates a bit). Thus, 500 mice would be the _____ of the field being studied.
Mathematics
1 answer:
Montano1993 [528]3 years ago
5 0

Answer:

The 500 mice would be the carrying capacity of the field being studied.

Step-by-step explanation:

For the first year of study, the mouse population demonstrates exponential growth.

But by third year, the mouse population has stabilized at approximately 500 mice.

Thus, this 500 mice would be the carrying capacity of the field being studied.

Carrying capacity is defined as the measure to demonstrate the maximum population size that any given environment can sustain for an unspecified time period.

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3q(p-q)+2r(p-q)-S(q-p)<br> Can u solve it step by step
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Answer:

-3q² + 3qp + 2rp - 2rq + Sq - Sp

Step-by-step explanation:

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3q(p-q) = 3qp - 3q²

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S(q-p) = Sq - Sp

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-3q² + 3qp + 2rp - 2rq + Sq - Sp

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Step-by-step explanation:

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solmaris [256]

Answers:

  1. Exponential and increasing
  2. Exponential and decreasing
  3. Linear and decreasing
  4. Linear and increasing
  5. Exponential and increasing

=========================================================

Explanation:

Problems 1, 2, and 5 are exponential functions of the form y = a(b)^x where b is the base of the exponent and 'a' is the starting term (when x=0).

If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.

If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.

In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.

Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.

---------------------

Problems 3 and 4 are linear functions of the form y = mx+b

m = slope

b = y intercept

This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.

If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.

On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.

Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.

7 0
1 year ago
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