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Chapter 4: Problem 75

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I used an exponential function to model Russia's declining population, the growth rate \(k\) was negative.

Short Answer

Expert verified
The statement makes sense. Using an exponential function with a negative growth rate is an appropriate model for a declining population.

Step by step solution

01

Understanding the statement

The statement is discussing an exponential function being used to model Russia's declining population with a negative growth rate. The key concept here is understanding how an exponential function works.
02

Interpreting the exponential function

In an exponential function, the rate of change or 'growth rate' may be positive or negative. A positive growth rate means the quantity is increasing over time, while a negative growth rate indicates it is decreasing over time. This decrease over time is often referred to as exponential decay.
03

Evaluating the statement's sense

So, when applying this concept to the statement 'When I used an exponential function to model Russia's declining population, the growth rate \(k\) was negative.', it makes sense. An exponential function with a negative growth rate is a reasonable way to model a declining population, such as what's being described regarding Russia's population. The negative growth rate suggests that the population is experiencing exponential decay, which is coherent with the description of a declining population.

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Most popular questions from this chapter

Explaining the Concepts What is the half-life of a substance?

The exponential growth models describe the population of the indicated country, \(A,\) in millions, t years after 2006 . $$ \begin{array}{ll} {\text { Canada }} & {A=33.1 e^{0.009 t}} \\ {\text { Uganda }} & {A=28.2 e^{0.034 t}} \end{array} $$ Use this information to determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The models indicate that in 2013 , Uganda's population will exceed Canada's.

The exponential growth models describe the population of the indicated country, \(A,\) in millions, t years after 2006 . $$ \begin{array}{ll} {\text { Canada }} & {A=33.1 e^{0.009 t}} \\ {\text { Uganda }} & {A=28.2 e^{0.034 t}} \end{array} $$ Use this information to determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Uganda's growth rate is approximately 3.8 times that of Canada's.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \ln \sqrt{2}=\frac{\ln 2}{2} $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. After 100 years, a population whose growth rate is \(3 \%\) will have three times as many people as a population whose growth rate is \(1 \%\)
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