Problem 75 - Algebra and Trigonometry

Question

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.

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.