Use a numerical example to explain the difference between the rate of change and the level of change between two values.

Q: What is the difference between the average rate of change and instantaneous rate of change?

A: The difference between the average rate of change and instantaneous rate of change

Q: Snowballs formed by kids in winter season is found to melt in such a way that the rate of change in…

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Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A: GIven: Altitude is increasing at a rate of 1 cm/min Area is increasing at a rate of 4.5 sq. cm/min…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Given Data: The increasing rate of the altitude of the triangle is: dhdt=3 cm/min The increasing…

Q: How does the average rate of change differ for a linear function versus an increasing exponential…

A: Given two function a linear function and an exponential function.

Q: What does it mean if two quantities vary directly? Explain.

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Q: A square has a side length that is decreasing at a rate of 8 cm per second. What is the rate of…

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Q: a) What is the change on surface area of a sphere as the radius changes from 1 inch to 3 inches? b)…

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Q: Estimate the instantaneous rate of change at x=2. Thank you

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Q: The area of a square is increasing at a rate of 60 centimeters squared per second. Find the rate of…

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Q: The sides of an equilateral triangle are increasing at the rate of 3 cm/min. Find the rate of the…

A: Given,          The sides of an equilateral triangle are increasing at the rate of 3 cm/min.…

Q: Compare Rates of Change and Tangent Lines?

A: Rates of change: The rates of changes of function f(x) on an interval [a, b] is the slope of the…

Q: How does related rates apply in real life situations?

A: The related rate is a concept that involves how the rate of two or more than two changing quantities…

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A: Let h be the altitude, b be the base and A be the area of the triangle at any time t. Given that,…

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A: Given that  the altitude of a triangle increases at the rate of 1 cm/min while the area of the…

Q: What kind of situation would be described by a positive rate of change for a pool context (volume of…

A: To write that what kind of situation is described by the positive rate of change for a pool.

Q: Find the rate of change. Express your result as a fraction. Snow is 2 inches deep after 1 hour and 5…

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Q: what are linear functions and their rate of change?

A: Linear functions  linear function whose graph is a straight line and contain one dependent and one…

Q: The instantaneous rate of change can never be zero. True False

A: The given statement, The instantaneous rate if change can never be zero, is False.

Q: Find the rate of change between (2,3) and (-4,-1) Rate of change =

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Q: The radius of a sphere is increasing at a rate of 3 inches per minute. Find the rate of change of…

A: Given, drdt = 3 inchmindVdt = ?    when r = 10 inches.

Q: The radius of a sphere is increasing at a rate of 4 inches per minute. Find the rate of change of…

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Q: How can I find the average rate of change?

A: Given that:f(x)=2x2-x+1 ;          x=0, x=3

Q: Find the net change and the average rate of change of f between x -5 and x = 6.

A: We have given the graph;

Q: Does nausea appear to be a problematic adverse reaction? Since the rate of nausea appears to be…

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Q: when its height is 6 centimeters.

A: Given that: The height of an equilateral triangle is decreasing at a rate of 0.5 centimeter per…

Q: One airplane is approaching an airport from the north at 128 km/hr. A second airplane approaches…

A: Let x be the distance of south bound plane and y be the distance of west bound plane from airport at…

Q: Explain : What is the average rate of change of a function?

A: Average rate of change: The average rate of change of a function is defined as the average rate at…

Q: The initial bacterium count in a culture is 2300. A biologist later makes a sample count of bacteria…

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Q: A researcher tells you that there are non-linearities in the relationship between wages and years of…

A: According to the provided information, it is mentioned by the researcher that there are…

Q: Explain the difference between the positive, negative, and constant rate of change?

A: we need to explain the difference between the positive, negative, and constant rate of change.

Q: Explain how to find the average rate of change of a function f between x =a and x =b.

A: Explain the average rate of change of a function f between x =a and x = b

Q: The humidity is currently 55% and falling at a rate of 4 percentage points per hour. (a) Estimate…

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Q: Is the rate of change in cost constant with respect to the number of pencils bought? Explain.

A: Yes, the rate of change of cost is constant with the rate of change of pencil.

Q: Determine the average rate of change of the function

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Q: What is the instantaneous rate of change?

A: Solution;-  Definition of Instantaneous rate of change:-

Q: Distinguish between AVERAGE and INSTANTANEOUS rate of change.

A: We want to distinguish the instantaneous rate of change and average rate of change

Q: Define the term instantaneous rates of change?

A: Given: Define the term instantaneous rates of change?

Q: 3. The amount of pollution x miles downwind of an electrical plant is g (x) = 64x¬4 + 8x parts per…

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Q: Part C: How does the average rate of change of the function change across the interval 0Sx < 20?

A: Given graph is  Part A- From the graph, it can be observed that the maximum value of the function…

Q: The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the…

A: Consider, the altitude of a triangle is "h" ,the base of triangle is "b"and the area of triangle is…

Q: What is the relationship between a function’s average and instan-taneous rates of change? Give an…

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Q: The radius of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of…

A: V= 43πr3 Here V is the volume and r is the radius.

Q: A deep sea diving bell is being lowered at a constant rate. After 10 minutes, the bell is at a depth…

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Q: A sky diver falls 200 meters in 20 seconds. He starts at 0 when he jumps out of the plane. Calculate…

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Q: The area of a square is increasing at a rate of 80 centimeters squared per second. Find the rate of…

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Q: The radius of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of…

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Q: What is the rate of change of the function

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Q: Last week's production at Morton Manufacturing was 1,600 units. This week the factory produced 1,913…

A: Given, Last week's production = 1600 units Current week's production = 1913 units

Exponential Growth Model

The relation that represents an exponential function is: