Pre-Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane SterlingЧитать онлайн книгу.

You buy a car that costs $23,495, and it loses $4,500 in value when you drive it off the car lot. The car then loses 10.785% in value each year (exponential depreciation). Rounded to the nearest cent, what is the value of the car after 5 years? Use the exponential equation math

, where y is the resulting value, C is the initial amount, k is the growth or decay rate, and t is the time in years.

386. A normal conversation is 60 decibels (dB). What is the intensity of the sound of the conversation (in watts per square meter)? Use the following formula, where L is decibels and I is the intensity of the sound: math .

387. Two earthquakes occurred in different parts of the country. The first earthquake had a magnitude of 8.0, and the second had a magnitude of 4.0. Compare the intensity of the earthquakes using the equation math , where M is the magnitude, I is the intensity measured from the epicenter, and I₀ is a constant.

388. A town had a population of 6,250 in 1975 and a population of 8,125 in 2010. If the rate of growth is exponential, what will the population be in 2040? Use the exponential model math , where y is the resulting population, C is the initial amount, k is the growth or decay rate, and t is the time in years.

389. In 2000, a house was appraised at $179,900. In 2013, it was reappraised at $138,000. If the decline rate is exponential, what will the value of the house be in 2020? Round the value to the nearest dollar. Use the exponential model math , where y is the resulting value, C is the initial amount, k is the growth or decay rate, and t is the time in years.

390. One student with a contagious flu virus goes to school when they’re sick. The school district includes 7,500 students and 1,000 staff members. The growth of the virus is modeled by the following equation, where y is the number infected and t is time in days: math . When 45% of the students and staff members fall ill, the schools will close. How many days before the schools are closed? Round to the nearest whole day.

Chapter 7

Trigonometry Basics

Trigonometric functions are special in several ways. The first characteristic that separates them from all the other types of functions is that input values are always angle measures. You input an angle measure, and the output is some real number. The angle measures can be in degrees or radians — a degree being one-360th of a slice of a circle, and a radian being about one-sixth of a circle. Each type has its place and use in the study of trigonometry.

Another special feature of trig functions is their periodicity; the function values repeat over and over and over, infinitely. This predictability works well with many types of physical phenomena, so trigonometric functions serve as models for many naturally occurring observations.

The Problems You’ll Work On

In this chapter, you’ll work with trigonometric functions and their properties in the following ways:

Defining the basic trig functions using the sides of a right triangle

Expanding the input values of trig functions by using the unit circle

Exploring the right triangle and trig functions to solve practical problems

Working with special right triangles and their unique ratios

Changing angle measures from degrees to radians and vice versa

Determining arc length of pieces of circles

Using inverse trig functions to solve for angle measures

Solving equations involving trig functions

What to Watch Out For

Don’t let common mistakes trip you up; keep in mind that when working with trigonometric functions, some challenges will include the following:

Setting up ratios for the basic trig functions correctly

Recognizing the corresponding sides of right triangles when doing applications

Remembering the counterclockwise rotation in the standard position of angles

Measuring from the terminal side to the x-axis when determining reference angles

Keeping the trig functions and their inverses straight from the functions and their reciprocals