1) Describe how you could use the graph of f(x) = 2x to obtain a decimal approximation for 2.2)I’m using a photocopier to reduce an image over and over by 75%, so the exponential function f(x) = (¾)x models the new image size, where x is the number of reductions. Determine whether this makes sense or not, and explain your reasoning.3)A rabbit population can increase at a rapid rate if left unchecked. Assume that 10 rabbits are put in an enclosed wildlife ranch and the rabbit population triples each year for the next 5 years. Let y represent the number of rabbits after x years. 4)A group of rabbits of a different kind is placed in a second enclosed wildlife ranch. This new population of rabbits doubles each year if left unchecked. Which of the following statements must be true about the model for the new rabbit population compared to the model you developed for the original rabbit population? Select all that apply.The base will change from 3 to 2.The coefficient will become 2.The y-intercept will be different.The function rule will be quadratic.As the number of years increases, the graph of this model will be less steep than the graph of the original model.As the number of years increases, the graph of this model will be steeper than the graph of the original model. 5)Compare the two rabbit population models in problem 3. How many rabbits would you need to start with in the new rabbit population to have at least the same number of rabbits as in the original model after 5 years? Clearly explain how you found your answer.6)

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1) Describe how you could use the graph of f(x) = 2x to obtain a decimal approximation for 2.

I’m using a photocopier to reduce an image over and over by 75%, so the exponential function f(x) = (¾)x models the new image size, where x is the number of reductions. Determine whether this makes sense or not, and explain your reasoning.

A rabbit population can increase at a rapid rate if left unchecked. Assume that 10 rabbits are put in an enclosed wildlife ranch and the rabbit population triples each year for the next 5 years. Let y represent the number of rabbits after x years.

A group of rabbits of a different kind is placed in a second enclosed wildlife ranch. This new population of rabbits doubles each year if left unchecked. Which of the following statements must be true about the model for the new rabbit population compared to the model you developed for the original rabbit population? Select all that apply.

The base will change from 3 to 2.
The coefficient will become 2.
The y-intercept will be different.
The function rule will be quadratic.
As the number of years increases, the graph of this model will be less steep than the graph of the original model.
As the number of years increases, the graph of this model will be steeper than the graph of the original model.

Compare the two rabbit population models in problem 3. How many rabbits would you need to start with in the new rabbit population to have at least the same number of rabbits as in the original model after 5 years? Clearly explain how you found your answer.

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