[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-508187-105":59,"doc-detail-508187-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","exponential-growth-and-decay-pert-math-section-112","Exponential Growth and Decay - PERT Math Section 11.2","","Exponential Growth and Decay practice sheet from PERT Math Section 11.2. It explains how exponential models multiply by a constant factor over equal input intervals, focusing on initial value, multiplier, and long-term behavior. Includes example evaluation, step-by-step guidance for identifying growth vs decay, plus 12 practice and word problems about growth/decay factors, percent change, and estimating values over time. Answer keys and reasoning steps support student mastery.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/exponential-growth-and-decay-pert-math-section-112/508187/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/exponential-growth-and-decay-pert-math-section-112/508187.png","ImageObject",300,407,{"name":92,"@type":93},"Valentina","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-05",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you decide whether an exponential model shows growth or decay?","Question",{"text":112,"@type":113},"Use the multiplier: if it is greater than 1, the values grow; if it is between 0 and 1, the values decay. Compare the base to 1 to judge each step.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What growth factor corresponds to increasing by 5% each year?",{"text":117,"@type":113},"A 5% increase means multiplying by 1 + 0.05 = 1.05 each year. So the model uses a factor of 1.05 per time interval.",{"name":119,"@type":110,"acceptedAnswer":120},"How can you write a decay model when a value loses a given percent each year?",{"text":121,"@type":113},"Convert the loss to the remaining percent. If 12% decays, 88% remains, so the yearly multiplier is 0.88 and the model multiplies by 0.88 each year.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},508187,1791503669,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":39,"preview_page_count":4},13056703020460,"https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923","Practice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nExponential Growth and Decay  \nPERT Math 􀀏 Section 11.2  \n\n| Name:   | D | ate:   | S | core:   / 12 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nExponential models multiply by a constant factor over equal input intervals. Compare the initial value, multiplier, and long-term behavior before deciding what the model means.  \n▷ Example: Evaluate 100(1.05)2 .  \nWork: Square the growth factor: 1.052 = 1 .1025. Then multiply: 100(1 . 1025) = 110 .25.  \n⋆ Answer: 110.25  \n♦ Practice Problems  \nSolve each problem. Show enough work that another student could follow your thinking.  \n1. Write a growth model for 200 increasing by 5% each year. 6. Find the decay factor for 35% decay.  \n2. Write a decay model for 800 decreasing by 12% each year. 7. Does y = 4(1 .2)x show growth or decay?  \n3. Evaluate 500(1 . 1)2 .  \n8. Does y = 9(0 .75)x show growth or decay?  \n4. Evaluate 1000(0 .9)3 .  \n9. Find the initial value of A = 350(1 .04)t .  \n5. Find the growth factor for 7% growth.  \n10. What is the percent change in y = 60(1 . 18)x?  \n♦ Word Problems  \n11. A car worth $20 ,000 loses 15% yearly. Write the model.  \n12. A population of 1 ,500 grows by 3% each year. Estimate after 2 years.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n1.  200(1 .05)t  7. Growth  \n2. 800(0 .88)t 8. Decay  \n3. 605 9. 350  \n4. 729 10.  18% growth   \n5. 1.07 11.  20000(0 .85)t  6. 0.65 12.  1 ,591.35   \nStep-by-Step Explanations  \n1. Going up 5% means you keep the whole amount plus a little more, so multiply by 1.05 every year.  \n2. Losing 12% leaves 88% behind, so the yearly multiplier is 0.88.  \n3. Two years of growth means multiplying by 1.1 twice: 1.12 = 1 .21, and  \n500 􀀂 1.21 = 605 .  \n4. Apply the 0.9 factor three times—0.93 = 0 .729—so 1000 shrinks to 729.  \n5. The factor is your starting whole, 1, plus the 0.07 you gain—so 1.07.  \n6. If 35% disappears, 65% stays—and that surviving share, 0.65, is your factor.  \n7. A base bigger than 1 makes each step larger than the last, so this one is growing.  \n8. When the base sits between 0 and 1, every multiply shrinks the value —that’s decay.  \n9. At t = 0 the factor 1.040 equals 1, so the coef􀀂cient 350 is exactly where things start.  \n10. Read 1.18 as 1 + 0.18—that extra 0.18 is an 18% jump each step.  \n11. Drop 15% and 85% of the value carries over, so each year multiplies by 0.85.  \n12. Two years of 3% growth means 1500 􀀂 1.032 ; since 1.032 = 1 .0609, you land at 1591.35.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s]","cbCaimHA9qchMjSh","https://ap.wps.com/l/cbCaimHA9qchMjSh","pdf",102697,"English","# Quick Review and Helpful Hints\n# Practice Problems\n# Word Problems\n# Answer Keys\n# Step-by-Step Explanations","[{\"question\":\"How do you decide whether an exponential model shows growth or decay?\",\"answer\":\"Use the multiplier: if it is greater than 1, the values grow; if it is between 0 and 1, the values decay. Compare the base to 1 to judge each step.\"},{\"question\":\"What growth factor corresponds to increasing by 5% each year?\",\"answer\":\"A 5% increase means multiplying by 1 + 0.05 = 1.05 each year. So the model uses a factor of 1.05 per time interval.\"},{\"question\":\"How can you write a decay model when a value loses a given percent each year?\",\"answer\":\"Convert the loss to the remaining percent. If 12% decays, 88% remains, so the yearly multiplier is 0.88 and the model multiplies by 0.88 each year.\"}]","Exponential Growth and Decay - PERT Math Section 11.2 | PDF",1791212326]