[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522930-105":59,"doc-detail-522930-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-solve-each-exponential-growthdecay-problem","Exponential Growth and Decay - Solve Each Exponential Growth/Decay Problem","","Worksheets problems on exponential growth and decay modeled by rates proportional to the current quantity. Includes population growth on an island with a specified percent per year, bacterial growth during an exponential phase, and exponential decay for Carbon-14. Also covers continuous compounding in a savings account to reach a target balance and Newton-style cooling of coffee modeled by a rate proportional to temperature difference from a constant room temperature.",{"@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-solve-each-exponential-growthdecay-problem/522930/",{"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-solve-each-exponential-growthdecay-problem/522930.png","ImageObject",300,407,{"name":92,"@type":93},"Melati","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is the island population growth modeled in this worksheet?","Question",{"text":112,"@type":113},"The growth rate is proportional to the current population, using the given percent per year and the current population to compute the population after a specified number of years.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What decay model is used for Carbon-14?",{"text":117,"@type":113},"Carbon-14 decays at a rate proportional to the amount present, using the given percent per thousand years and the current mass to find the mass after a specified time.",{"name":119,"@type":110,"acceptedAnswer":120},"How is continuous compounding for the savings account handled?",{"text":121,"@type":113},"The balance grows using continuous compounding at the stated annual interest rate, and the problem asks for the time needed to reach the target balance.","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},522930,1791506958,{"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":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"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":24,"preview_page_count":4},962085570644,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Kuta Software-Infinite Calculus  \nExponential Growth and Decay  \nSolve each exponential growth/decay problem.  \n1) For a period of time, an island's population grows at a rate proportional to its population. If the growth rate is 3.8% per year and the current population is 1543, what will the population be 5.2 years from now?  \n3) Radioactive isotope Carbon-14 decays at a rate proportional to the amount present. If the decay rate is 12.10% per thousand years and the current mass is 135.2 mg, what will the mass be 2.2 thousand years from now?  \n5) A cup of coffee cools at rate proportional to the difference between the constant room temperature of 20.0°C and the temperature of the coffee. If the temperature of the coffee was 86.1°C 3.0 minutes ago and the current temperature of the coffee is 79.9°C, what will the temperature of the coffee be 29.0 minutes from now?  \nName  Date  Period   \n2) During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now?  \n4) A savings account balance is compounded continuously. If the interest rate is 3.1% per year and the current balance is $1077 .00, in how many years will the balance reach $1486.73?  \n6) During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the population doubles in 20.4 minutes, in how many minutes will the population triple?  \nKuta Software-Infinite Calculus  \nExponential Growth and Decay  \nSolve each exponential growth/decay problem.  \n1) For a period of time, an island's population grows at a rate proportional to its population. If the growth rate is 3.8% per year and the current population is 1543, what will the population be 5.2 years from now?  \n􀀔􀀘􀀗􀀖 e 􀀓􀀑􀀓􀀖􀀛 􀂘 􀀘􀀑􀀕 􀁼 􀀔􀀛􀀛􀀓  \n3) Radioactive isotope Carbon-14 decays at a rate proportional to the amount present. If the decay rate is 12.10% per thousand years and the current mass is 135.2 mg, what will the mass be 2.2 thousand years from now?  \n􀀔􀀖􀀘􀀑􀀕 e 􀀐􀀓􀀑􀀔􀀕􀀔 􀂘 􀀕􀀑􀀕 􀁼 􀀔􀀓􀀖􀀑􀀙 mg  \n5) A cup of coffee cools at rate proportional to the difference between the constant room temperature of 20.0°C and the temperature of the coffee. If the temperature of the coffee was 86.1°C 3.0 minutes ago and the current temperature of the coffee is 79.9°C, what will the temperature of the coffee be 29.0 minutes from now?  \nln 􀀘􀀙~~ ~~􀀜􀀙~~ ~~􀀑􀀑~~ ~~􀀜􀀔~~ ~~  \n~~ ~~ 􀂘 􀀕􀀜  \n􀀕􀀓 􀀎 􀀘􀀜􀀑􀀜 e 􀀖 􀁼 􀀗􀀖􀀑􀀔 °C  \nName  Date  Period   \n2) During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now?  \n􀀔􀀚􀀕 e 􀀓􀀑􀀓􀀔􀀜 􀂘 􀀚􀀑􀀕 􀁼 􀀔􀀜􀀚􀀑􀀕 million  \n4) A savings account balance is compounded continuously. If the interest rate is 3.1% per year and the current balance is $1077 .00, in how many years will the balance reach $1486.73?  \nln ~~ ~~􀀔~~ ~~􀀗􀀔􀀛􀀓􀀙􀀚􀀑􀀚􀀚~~ ~~􀀖~~  ~~ 􀀓􀀑􀀓􀀖􀀔  􀁼 􀀔􀀓􀀑􀀗 yr  \n6) During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the population doubles in 20.4 minutes, in how many minutes will the population triple?  \n 􀀕􀀓􀀑􀀗 ln 􀀖   \n􀁼 􀀖􀀕􀀑􀀖 min ln 􀀕  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaifsbuxgqxKex","https://ap.wps.com/l/cbCaifsbuxgqxKex","pdf",21510,"English","# Exponential Growth and Decay Problems\n## Population and biological growth\n## Radioactive decay\n## Cooling models\n## Continuous compounding and tripling time","[{\"question\":\"How is the island population growth modeled in this worksheet?\",\"answer\":\"The growth rate is proportional to the current population, using the given percent per year and the current population to compute the population after a specified number of years.\"},{\"question\":\"What decay model is used for Carbon-14?\",\"answer\":\"Carbon-14 decays at a rate proportional to the amount present, using the given percent per thousand years and the current mass to find the mass after a specified time.\"},{\"question\":\"How is continuous compounding for the savings account handled?\",\"answer\":\"The balance grows using continuous compounding at the stated annual interest rate, and the problem asks for the time needed to reach the target balance.\"}]","Exponential Growth and Decay - Solve Each Exponential Growth/Decay Problem | PDF",1791426318]