/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 5 Budget cuts have severely crippl... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 5

Budget cuts have severely crippled your department over the last few years. Your operating budget of \(\$ 600,000\) has decreased by \(5 \%\) each of the last 3 years. What is your current operating budget?

Short Answer

Expert verified
Answer: The current operating budget is $514,425.

Step by step solution

01

Understand the problem

We need to determine the current operating budget after a 5% decrease for each of the last 3 years. Our initial budget is $600,000. To solve this, we will apply the formula for compound percentage decrease.
02

Apply the formula for compound percentage decrease

The formula for compound interest (or percentage change) is: \(A = P(1 + r/n)^{nt}\) where \(A\) is the final amount (current operating budget), \(P\) is the initial amount (initial budget), \(r\) is the annual interest rate (in our case, the percentage decrease as a decimal), \(n\) is the number of times the interest is compounded per year, and \(t\) is the number of years. However, in this scenario, the decrease is compounded every year. So we can simplify the equation as: \(A = P(1 + r)^t\) For our problem, \(P = 600,000\), \(r = -0.05\) (a decrease is represented by a negative value), and \(t = 3\).
03

Calculate the current operating budget

Using the formula and values provided, we can calculate the current operating budget: \(A = 600,000(1 - 0.05)^3\) \(A = 600,000(0.95)^3\) \(A = 600,000 \times 0.857375\) \(A = 514,425\) So, the current operating budget is \(\$514,425\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the conversion tables or formulas on the inside back cover of the textbook for conversion equivalencies. Powdered skim milk sells for \(\$ 6.99\) a box in the supermarket. The amount in the box is enough to make 8 quarts of skim milk. What is the price for 12 quarts of skim milk prepared in this way?

The customary tip on waiter service in New York City restaurants is approximately \(20 \%\) of the food and beverage cost. This means that your server is counting on a tip of \(\$ 0.20\) for each dollar you spend on your meal. What is the expected tip on a dinner for two costing \(\$ 65 ?\)
The admissions office in a local college has organized data in the following table listing the number of men and women who are currently enrolled. Admissions will use the data to help recruit students for the next academic year. Note that a student is matriculated if he or she is enrolled in a program that leads to a college degree. $$\begin{array}{|c|c|c|} \hline {} & \text { FULL-TIME } & \text { PART-TIME } & \text { PART-TIME } \\\ {} & \text { MATRICULATED } & \text { MATRICULATED } & \text { NONMATRICULATED} \\\ {} & \text { STUDENTS } & \text { STUDENTS } & \text { STUDENTS } \\\ {} & ( \geq 12 \text { Credits) } & ( < 12 \text { Credits) } & ( < 12 \text { Credits) } \\\\\hline \text { Men } & 214 & 174 & 65 \\\ \hline \text { Women } & 262 & 87 & 29 \\\ \hline \end{array}$$ a. How many men attend the college? b. What percent of the men are full-time students? c. How many women attend the college? d. What percent of the women are full-time students? e. Write the ratio of men to women verbally and as a fraction. f. How many students are enrolled full-time? g. How many students are enrolled part-time? h. Write the ratio of part-time students to full-time students verbally and as a fraction. i. What percent of the full-time students are women? j. What percent of the part-time students are women? k. How many students are nonmatriculated? l. Write the ratio of nonmatriculated men to matriculated men verbally and as a fraction. m. What percent of the student body is nonmatriculated?
a. In \(2008,\) new car and truck sales totaled approximately \(13,250,000\) in the United States. The breakdown among the leading automobile manufacturers was General Motors \(22.3 \%\) Ford \(15.2 \%\) Chrysler \(11 \%\) Approximately how many new cars did each U.S. company sell that year? b. Toyota sold \(2,217,660\) vehicles in \(2008 .\) What was its market share?
A company that manufactures optical products estimated that three out of five people in North America wear eyeglasses. The population of North America was projected to be about 540 million in 2010 . Use a proportion to estimate the number of people in North America who were expected to wear eyeglasses in 2010 .
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.