# Chapter 2 Topics

2.1 Percent Change

2.2 Averages

2.3 Ratios, Proportions, and Prorating

Basic calculations are so much a part of your everyday life that you could not escape them if you tried. While driving to school, you may hear on the radio that today’s forecasted temperature of 27°C is 3°C warmer than the historical average. In the news, consumers complain that gas prices rose 11% in three months. A commercial tells you that the Toyota Prius you are driving uses almost 50% less gas than the Honda Civic Coupe Si. After class you head to Anytime Fitness to cancel a gym membership because you are too busy to work out. You have used only four months of an annual membership for which you paid \$449, and now you want to know how large a prorated refund you are eligible for.

On a daily basis you use basic calculations such as averages (the temperature), percent change (gas prices), ratios and proportions (energy efficiency), and prorating (the membership refund). To invest successfully, you must also apply these basic concepts. Or if you are an avid sports fan, you need basic calculations to understand your favourite players’ statistics.

It’s not hard to see how these calculations would be used in the business world. Retail managers can use historical average data to predict future sales, as well as effectively assign employees to service those sales. Human resource managers continually calculate ratios between accounting and performance data to assess how efficiently labour is being used. Managers proration a company’s budget across its various departments.

This chapter covers universal business mathematics. You will use these concepts and the skills you gain whether your chosen business profession is marketing, accounting, production, human resources, economics, finance, or something else altogether. To be a successful manager you need to understand percent changes, averages, ratios, proportions, and prorating.

\begin{align*} 1.05^x=0.292741&\Rightarrow \ln 1.05^x=\ln 0.292741\\ &\Rightarrow x\ln 1.05=\ln 0.292741\\ &\Rightarrow x=\frac{\ln 0.292741}{\ln 1.05}\approx -25.178579 \end{align*}

#### Paths To Success

You do not have to memorize the mathematical constant value of $e$. If you need to recall this value, use an exponent of 1 and access the $e^x$ function on your calculator. Hence, $e^1 = 2.71828182845$.

#### Concept Check

Try out your understanding of properties of logarithms:

MathMatize: Properties of logarithms

#### Give It Some Thought

For each of the following powers, determine if the natural logarithm is positive, negative, zero, or impossible.