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Given that 1+t,1+2t,and 1+3t2 are solutions to the

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 35E Chapter 4.7

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 35E


Given that 1+t,1+2t,and 1+3t2 are solutions to the differential equation  find the solution to this equation that satisfies y(1) = 2, y’(1) = 0.

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Advertising Chapter 15 Notes: Part 5: Integrated Brand Promotion Sales Promotion: using incentives to create a perception of greater brand value • Consumer market – induce household consumers to purchase a firm’s brand • Trade-Market – motivate distributors, wholesalers, and retailers to stock and feature a brand • Business market – cultivate buyers in large corporations who make purchase decisions Sales promotion examples: • Loyalty programs, brand placements, contests, trade shows, coupons, gift cards, allowance, sweepstakes, incentives, point of purchase displays, sampling, price- off deals, premiums, What is the difference between advertising and sales promotion • Sales Promotion: 1. Short-term demand 2. Encourages brand switching 3. Induces trial use (vs repeat use, bargain/incentive) 4. Promotes price (consumers are price sensitive) 5. Immediate results (converts to sales quick) 6. Measurable results (ie number of coupons redeemed) • Advertising: 1. Long-term demand 2. Brand loyalty 3. Encourage repeat purchase 4. Maintains Brand Image 5. Long-term effects 6. Difficult to measure (if ads turn into sales) Importance and growth of the use of sales promotion • Reasons for growth: o Demand for accountability o Short-term orientation o Consumer response to promotions o Proliferation of brands (choose brand on sale) o Increased power of retailers (certain promotions only available at Target) o Media clutter (sale promotions break through clutter, at point of purchase) • Push strategy – involves convincing trade channel members to “push; the product through the distribution channels to the ultimate consumer via promotions and personal selling efforts • Pull strategy – attempts to get consumers to “pull” the product from the manufacturer through the marketing channel. The company focuses its marketing communication efforts on consumers in the hope that it stimulates interest and demand for the product at the end-user level. Objectives for consumer-market sales promotion: 1. Stimulate trial purchase 2. Stimulate repeat purchases 3. Stimulate larger purchases (larger size keeps consumer out of needing category, in turn not buying completion for that time period) 4. Introduce a new brand/product 5. Combat or disrupt competitors 6. Contribute to IBP effort • ^^^ all of the above happens on Black Friday Consumer-Market sales promotion techniques: 1. Coupons a. Only offer lower price to coupon holders, everyone else pays regular b. Stimulate repeat purchases c. Get regular user to trade up • Disadvantages of Coupons: o Timing of redemption cannot be controlled –no control over when consumer redeems it; can be used with other promotions o No way of preventing current brand loyal customers from redeeming coupons o Coupon programs require costly preparation 2. Price-off deal – money taken off at point of sale a. Typically for specially marked packages b. Deduction taken from manufacturer’s profit c. Often marked at 10% -20% off d. Can affect positive price comparisons e. Can create inventory problems for retailers 3. Premiums – offered for free or at a reduced price with the purchase of another item a. Self-liquidating premium – cigarettes with t-shirt b. Brand loyal massages – messages placed on item with no obligation (ie free sponge with Mr. clean) 4. Contests/sweepstakes a. Contest – consumer competes for prize b. Sweepstakes – by chance, equal opportunity c. Extremely regulated, potential legal issues d. Does not guarantee sales ( no purchase necessary) 5. Samples and trials a. Samples – consumables b. Trials – more expensive, subscriptions 6. [Phone] gift cards a. ITunes cards, etc 7. Rebates a. Good for manufacturers – consumer buys at perceived lower price, but few send in rebate (forget, extra work, etc) b. Often for large ticket items or multiple purchases 8. Frequency programs – continuity program; a. Discounts or points given to multiple purchases b. Airlines, hotels Objectives for Promotions in the trade market • Objectives: uses push strategy – push the product into the distribution channel to the consumer o Obtain initial distribution o Increase order size – goal is for them to buy more o Encourage cooperation with consumer market sales promotions o Increase store traffic at retail Trade market sales promotion techniques: • Incentives: push money – manufacturer pays retailer more beforehand to place product • Allowances – o Merchandise allowances – products packed in regular shipments to maintain displays, sold at discount o Slotting fees – manufacturer pays retailer to maintain position on shelf; prime shelf space is at eye-level o Bill-back allowances – monetary incentives for featuring a brand in in-store displays or material; o Off-invoice allowances • Sales training programs • Cooperative advertising Business Market Sales Promotion Techniques: • Trade Shows • Business gifts o Used often in pharmaceuticals; ie samples, incentives o Don’t want to be viewed as paying someone to do business with you • Premiums and advertising specialties o Ie bobble heads at reds game • Trial offers o Suited for business market o Ie textbook to teacher, students have to buy • Benefits Program Risks of Sales Promotion • Create price orientation that conflicts brand image development o Ie higher end brand, but always on sale/never pay full price (Macy’s) • Borrow for future sales o Buy more now, consumer is not going to buy again until very later • Alienate loyal customers • Significant time and expense o Process of making and developing promotion is costly • Legal considerations Point-of-Purchase Advertising • P&G moment of truth – after all promotions this is the final chance to buy • Definition: materials used in the retail setting to attract shoppers’ attention to a brand to convey primary product benefit or highlight pricing information • Displays may feature “price off” deals as well • Firms starting to use mobile device distribution • Objectives for POP Advertising: o Draw consumers’ attention to a brand in the retail setting o Maintain loyalty among brand users o Stimulate increased or varied usage of the brand o Stimulate trial use by users of competitive brands § ie catching “switchers” POP and Mobile Location Marketing • Some argue that POP is mobile location marketing • But, new techniques allow sending POP offers through mobile devices • Consumer attitudes towards location marketing are still unknown • Examples: yelp, foursquare, SMS text offers • Those opposed – privacy issue, cluttered with offers/communications POP advertising and the trade and business markets • Product displays and information sheets encourage retailers to support one distributor or manufacturers’ brand over another • POP promotions can help win precious shelf space and exposure in a retail setting o Retailer will ensure that product is premium shelved during promotion period • A POP display should be designed to draw attention to a brand, increase turnover, and possibly distribute coupons or sweepstakes entry forms • To combat losing business to online shopping, retailers are trying to enliven the retail environment and POP displays are a key strategy Support Media: • Purpose: to reinforce or extend a message being delivered through other media • Examples: signs, billboard, posters • Transit and aerial advertising • Cinema Advertising Outdoor Signage and billboards • Advantages: o Wide local exposure o Can be captivating o Around the clock exposure o Can address an immediate need or desire o New digital technology being used • Disadvantages: o Message limits o Location affects impact (need traffic for more exposure) o Relatively expensive Transit Ads • Urban environments • Reasonable demographic segment • Good message repetition • Timely to purchase locations • Can subtlety build brand awareness Aerial Ads • Blimps increasingly common • Common at sporting events o Lots of people to see it o Digitl technology offers more creativity o Skies are getting crowded o Networks are in control ARI Cinema • On-screen and off-screen in theaters • Consumers say they are annoyed; go to theater to relax • Reasonable presence Directory Advertising • Advantages: o High acceptance o High availability o Final link to purchase • Disadvantages o Too many directories; yellow book and each telephone company o Long lead times for printed versions o Limited creativity Packaging: • Promotional benefits of packaging to the advertiser: o The package carries the brand name and logo o The package can communicate “value” o The package can communicate “image” and “quality” § Ie G2 packaging

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Chapter 4.7, Problem 35E is Solved
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Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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Given that 1+t,1+2t,and 1+3t2 are solutions to the