[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522614-105":59,"doc-detail-522614-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","continuous-exponential-growth-and-decay-exponential-growthdecay-problems","Continuous Exponential Growth and Decay - Exponential Growth/Decay Problems","","Worksheet on continuous exponential growth and decay modeled with continuous compounding and continuous rate formulas. Students solve multiple real-world scenarios including a continuously compounded savings account, radioactive isotope decay using a continuous decay rate, and island population growth with exponential doubling intervals. Additional applications include exponential bacterial growth in minutes and pressure decrease with increasing elevation, requiring evaluation at specified time spans and distances. Graphs may be used to sketch functions and estimate values.",{"@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/continuous-exponential-growth-and-decay-exponential-growthdecay-problems/522614/",{"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/continuous-exponential-growth-and-decay-exponential-growthdecay-problems/522614.png","ImageObject",300,407,{"name":92,"@type":93},"River Wang","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you model continuous exponential growth or decay for these problems?","Question",{"text":113,"@type":114},"Use an exponential function with a continuous growth or decay rate, then substitute the given initial value and the target time (or distance) to compute the new quantity.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What continuous compounding formula is used for the savings account problems?",{"text":118,"@type":114},"Balance at a future time is computed with continuous compounding using the given annual interest rate, written in the form of an initial balance multiplied by an exponential factor.",{"name":120,"@type":111,"acceptedAnswer":121},"How is the radioactive decay problem solved using the continuous decay rate?",{"text":122,"@type":114},"Apply continuous decay by using the initial mass and the given decay rate, then evaluate the exponential expression at the specified number of thousand years.","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},522614,1791493308,{"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":19,"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":52,"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","Kuta Software-Infinite Algebra 2 Name   \nContinuous Exponential Growth and Decay Date  Period   \nSolve each continous exponential growth/decay problem. You may use the provided graph toplot points or sketch the exponential function.  \n1) A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1,854.00, what will the balance be 5 years from now?  \n2400  \n2000  \n1600  \n1200  \n800  \n400  \nbalance in dollars  \n1 2 3 4 5 6 year  \n3) For a period of time, an island's population grows exponentially. If the population doubles every 17 years and the current population is 1,725, what will the population be 10 years from now?  \n1 2 3 4 5 6 7 8 9 10 11 12 year  \n2) Radioactive isotope Berkelium-247 decays exponentially. If the continuous decay rate is 50% per thousand years and the current mass is 804.90 grams, what will the mass be 7 thousand years from now?  \n1 2 3 4 5 6 7 8 9 1000 yr  \n4) A savings account balance is compounded continuously. If the balance was $1, 183.63 8 years ago and the current balance is $1,389.00, what will the balance be 5 years from now?  \nbalance in dollars 1800  \n1600  \n1400  \n1200  \n1000  \n800  \n600  \n400  \n200  \n-10 -8 -6 -4 -2 2 4 6 year  \nSolve each continous exponential growth/decay problem.  \n5) For a period of time, E. coli bacteria in a culture grows exponentially. If the continuous growth rate is 1% per minute and the current population is 165.0 million, what will the population be 6 minutes from now?  \n7) A savings account balance is compounded continuously. If the balance doubles every 23 years and the current balance is $1,059.00, what will the balance be 6 years from now?  \n6) Atmospheric pressure decreases approximately exponentially as elevation increases. If the continuous rate of decrease is determined to be 12% per kilometer and the pressure at sea level is 751.0 mmHg, what is the pressure at 8.3 kilometers above sea level?  \n8) For a period of time, an island's population grows exponentially. If the population was 1, 128 6 years ago and the current population is 1,351, what will the population be 7 years from now?  \nKuta Software-Infinite Algebra 2 Name   \nContinuous Exponential Growth and Decay Date  Period   \nSolve each continous exponential growth/decay problem. You may use the provided graph toplot points or sketch the exponential function.  \n1) A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1,854.00, what will the balance be 5 years from now?  \n1 2 3 4 5 6  \n1854e0.03 × 5 ≈ $2, 154.04  \nyear  \n2) Radioactive isotope Berkelium-247 decays exponentially. If the continuous decay rate is 50% per thousand years and the current mass is 804.90 grams, what will the mass be 7 thousand years from now?  \n1 2 3 4 5 6 7 8 9 1000 yr  \n804.9e-0.5 × 7 ≈ 24.31 grams  \n3) For a period of time, an island's population grows exponentially. If the population doubles every 17 years and the current population is 1,725, what will the population be 10 years from now?  \n1 2 3 4 5 6 7 8  \n 10  \n1725 × 2 17 ≈ 2,593  \n9 10 11 12  \nyear  \n4) A savings account balance is compounded continuously. If the balance was $1, 183.63 8 years ago and the current balance is $1,389.00, what will the balance be 5 years from now?  \n-10 -8 -6 -4 -2 2 4 6  \n5  \nyear  \n1389 × (~~ ~~1113883963~~ ~~) 8 ≈ $1,535.08  \nSolve each continous exponential growth/decay problem.  \n5) For a period of time, E. coli bacteria in a culture grows exponentially. If the continuous growth rate is 1% per minute and the current population is 165.0 million, what will the population be 6 minutes from now?  \n165e0.01 × 6 ≈ 175.2 million  \n7) A savings account balance is compounded continuously. If the balance doubles every 23 years and the current balance is $1,059.00, what will the balance be 6 years from now?  \n 6   \n1059 × 223 ≈ $1,268.89  \n6) Atmospheric pressure decreases approximately exponentially as elevation increases. ","cbCairSOStbepACK","https://ap.wps.com/l/cbCairSOStbepACK","pdf",59944,"English","# Solve each continuous exponential growth/decay problem\n## Savings account continuously compounded balance\n## Radioactive isotope decay\n## Population exponential growth (island)\n## Bacterial exponential growth\n## Atmospheric pressure vs. elevation","[{\"question\":\"How do you model continuous exponential growth or decay for these problems?\",\"answer\":\"Use an exponential function with a continuous growth or decay rate, then substitute the given initial value and the target time (or distance) to compute the new quantity.\"},{\"question\":\"What continuous compounding formula is used for the savings account problems?\",\"answer\":\"Balance at a future time is computed with continuous compounding using the given annual interest rate, written in the form of an initial balance multiplied by an exponential factor.\"},{\"question\":\"How is the radioactive decay problem solved using the continuous decay rate?\",\"answer\":\"Apply continuous decay by using the initial mass and the given decay rate, then evaluate the exponential expression at the specified number of thousand years.\"}]","Continuous Exponential Growth and Decay - Exponential Growth/Decay Problems | PDF",1791425975]