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We are growing a population of bacteria in a jar.At 11:00am there is one bacterium in the jar, The bacteria divide once every minute so the population doubles every minute. At 12:00 noon the jar is full. At what time was the jar half-full?

We are growing a population of bacteria in a jar.At 11:00am there is one bacterium in the jar, The bacteria divide once every minute so the population doubles every minute. At 12:00 noon the jar is full. At what time was the jar half-full?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Could I have help with these three questions please

We are growing a population of bacteria in a jar.At 11:00am there is one bacterium in the jar, The bacteria divide once every minute so the population doubles every minute. At 12:00 noon the jar is full. At what time was the jar half-full?

The drawing represents a loaf of bread with a slice shown x inches from the left-hand end of the bread. Which of the following graphs could represent the volume V of the bread to the left of the slice as a function of the distance x from the left-hand end of the slice?

The derivative of a function f is given by f'(x)=ax^2+b. What is required of the values a and b so that the slope of the tangent line to f will be positive at x=0

 

 

**Transcription for Educational Use:** The illustration depicts a loaf of bread with a slice located \( x \) inches from the left-hand end. The question asks which of the given graphs could represent the volume \( V \) of the bread to the left of the slice as a function of the distance \( x \) from the left-hand end of the bread. **Diagrams and Graphs:** 1. **Top Diagram:** - A side view of a loaf of bread with a slice marked by a vertical line \( x \) inches from the left end. 2. **Graphs:** a) **Graph (a):** - The graph shows a function \( V(x) \) with the volume increasing quickly at first and then tapering off as \( x \) increases. The curve suggests a concave downwards shape as \( x \) grows. b) **Graph (b):** - In this graph, \( V(x) \) shows a consistent upward curve, starting slow and accelerating. The shape indicates an exponential increase in volume as \( x \) increases. c) **Graph (c):** - This graph depicts a rise and fall in the function \( V(x) \). It increases sharply, reaches a peak, and then decreases, suggesting a single maximum point. d) **Graph (d):** - Similar in shape to graph (c), this graph shows \( V(x) \) rising to a peak before gradually declining, indicating a volume increase that then contracts as \( x \) continues to grow. The task is to determine which graph accurately represents how the volume \( V \) of the bread to the left of the slice depends on the position of the slice, \( x \).
Transcribed Image Text:**Transcription for Educational Use:** The illustration depicts a loaf of bread with a slice located \( x \) inches from the left-hand end. The question asks which of the given graphs could represent the volume \( V \) of the bread to the left of the slice as a function of the distance \( x \) from the left-hand end of the bread. **Diagrams and Graphs:** 1. **Top Diagram:** - A side view of a loaf of bread with a slice marked by a vertical line \( x \) inches from the left end. 2. **Graphs:** a) **Graph (a):** - The graph shows a function \( V(x) \) with the volume increasing quickly at first and then tapering off as \( x \) increases. The curve suggests a concave downwards shape as \( x \) grows. b) **Graph (b):** - In this graph, \( V(x) \) shows a consistent upward curve, starting slow and accelerating. The shape indicates an exponential increase in volume as \( x \) increases. c) **Graph (c):** - This graph depicts a rise and fall in the function \( V(x) \). It increases sharply, reaches a peak, and then decreases, suggesting a single maximum point. d) **Graph (d):** - Similar in shape to graph (c), this graph shows \( V(x) \) rising to a peak before gradually declining, indicating a volume increase that then contracts as \( x \) continues to grow. The task is to determine which graph accurately represents how the volume \( V \) of the bread to the left of the slice depends on the position of the slice, \( x \).
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