[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-508186-105":59,"doc-detail-508186-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","comparing-linear-quadratic-and-exponential-models-practice-problems","Comparing Linear, Quadratic, and Exponential Models - Practice Problems","","Practice worksheet section comparing linear, quadratic, and exponential models. It provides quick review on exponential growth using constant multiplicative factors over equal input intervals, plus an worked example evaluating an expression like 100(1.05)^2. The main body includes practice questions to classify functions by constant first differences, constant second differences, and repeated percent growth, along with word problems involving savings interest, and bacterial doubling. An answer keys and step-by-step explanations follow.",{"@graph":69,"@context":123},[70,84,106],{"@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/comparing-linear-quadratic-and-exponential-models-practice-problems/508186/",{"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/comparing-linear-quadratic-and-exponential-models-practice-problems/508186.png","ImageObject",300,407,{"name":92,"@type":93},"River Wang","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-05",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do exponential models differ from linear models when comparing growth over time?","Question",{"text":113,"@type":114},"Exponential models multiply by a constant factor over equal input intervals, while linear models add the same amount each step. Given enough time, exponential growth eventually outpaces linear growth.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What test helps determine whether a function has constant first differences?",{"text":118,"@type":114},"Compute first differences from an evenly spaced input table; constant first differences indicate a linear model. If first differences change but settle in the second differences, the model is quadratic.",{"name":120,"@type":111,"acceptedAnswer":121},"Why does repeated percent growth correspond to an exponential model?",{"text":122,"@type":114},"Repeated percent growth applies the same multiplicative factor over and over. That repeated multiplying is the defining behavior of exponential functions.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},508186,1791503774,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":39,"preview_page_count":4},1099514067438,"https://ap-avatar.wpscdn.com/avatar/100002539ee87300030?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780474512215547542","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)  \nComparing Linear, Quadratic, and Exponential Models  \nPERT Math 􀀏 Section 11.3  \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. Which grows faster eventually: 5x + 20 or 2x ? 6. Which has a constant ratio in outputs?  \n2. Classify y = 3x + 7 . 7. Which model has constant 􀀂rst differences?  \n3. Classify y = x2 􀀀 4. 8. Compare at x = 3: f = x2 and g = 2x .  \n4. Classify y = 6(1 .4)x .  \n9. Compare at x = 5: f = 3x + 1 and g = x2 .  \n5. Which has constant second differences?  \n10. Which model can represent repeated percent growth?  \n♦ Word Problems  \n11. A savings account adds $50 monthly. Linear or exponential?  \n12. A bacteria culture doubles hourly. Linear, quadratic, or exponential?  \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. 2x 7. Linear  \n2. Linear 8.  f (3) = 9 is greater   \n3. Quadratic 9. g is greater  \n4. Exponential 10. Exponential  \n5.  Quadratic  11. Linear  \n6.  Exponential  12.  Exponential   \nStep-by-Step Explanations  \n1. Linear growth adds the same chunk each step, but exponential keeps multiplying—given time, it always wins.  \n2. The x sits at power 1 and the rate never changes, which is the signature of alinear function.  \n3. That x2 as the biggest power is the telltale sign—this one’s quadratic.  \n4. The variable is up in the exponent, which means the function grows by multiplying—that’s exponential.  \n5. In a quadratic table the 􀀂rst differences keep changing, but the differences of THOSE settle to a constant.  \n6. Step the input evenly and an exponential multiplies the output by the same factor each time—a steady ratio.  \n7. Even input steps produce even output steps in a linear function—the differences stay the same.  \n8. At x = 3 , 23 = 8 but 32 = 9—so this early, the quadratic is still ahead.  \n9. Plug in 5: the line gives 16 while the parabola gives 25, so g pulls ahead here.  \n10. Percent growth multiplies by the same factor over and over, and that repeated multiplying is exactly exponential.  \n11. The same $50 goes in every month—a 􀀂xed amount added repeatedly makes it linear.  \n12. Doubling each hour means multiplying by 2 again and again, and repeated multiplying is the heart of exponential. ","cbCaicSrY7b0WILs","https://ap.wps.com/l/cbCaicSrY7b0WILs","pdf",101515,"English","# Quick Review and Helpful Hints\n# Practice Problems\n# Word Problems\n# Answer Keys\n# Step-by-Step Explanations","[{\"question\":\"How do exponential models differ from linear models when comparing growth over time?\",\"answer\":\"Exponential models multiply by a constant factor over equal input intervals, while linear models add the same amount each step. Given enough time, exponential growth eventually outpaces linear growth.\"},{\"question\":\"What test helps determine whether a function has constant first differences?\",\"answer\":\"Compute first differences from an evenly spaced input table; constant first differences indicate a linear model. If first differences change but settle in the second differences, the model is quadratic.\"},{\"question\":\"Why does repeated percent growth correspond to an exponential model?\",\"answer\":\"Repeated percent growth applies the same multiplicative factor over and over. That repeated multiplying is the defining behavior of exponential functions.\"}]","Comparing Linear, Quadratic, and Exponential Models - Practice Problems | PDF",1791212325]