{"id":28663,"date":"2025-06-20T14:15:37","date_gmt":"2025-06-20T14:15:37","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28663"},"modified":"2025-06-20T14:15:43","modified_gmt":"2025-06-20T14:15:43","slug":"if-a-bacterial-culture-initially-contains-4-bacteria-and-has-a-generation-time-of-30-minutes","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/if-a-bacterial-culture-initially-contains-4-bacteria-and-has-a-generation-time-of-30-minutes\/","title":{"rendered":"If a bacterial culture initially contains 4 bacteria and has a generation time of 30 minutes"},"content":{"rendered":"\n<p>If a bacterial culture initially contains 4 bacteria and has a generation time of 30 minutes, how many bacteria will be present in the culture in 90 minutes? Assume that all bacteria survive.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s break down the problem step-by-step:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial number of bacteria, N0=4N_0 = 4<\/li>\n\n\n\n<li>Generation time = 30 minutes (time it takes for the bacteria population to double)<\/li>\n\n\n\n<li>Total time = 90 minutes<\/li>\n\n\n\n<li>Assume all bacteria survive and multiply<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">What is being asked?<\/h3>\n\n\n\n<p>Find the total number of bacteria NN present after 90 minutes.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the number of generations<\/h3>\n\n\n\n<p>Since bacteria double every generation time, the number of generations nn in 90 minutes is: n=total&nbsp;timegeneration&nbsp;time=9030=3&nbsp;generationsn = \\frac{\\text{total time}}{\\text{generation time}} = \\frac{90}{30} = 3 \\text{ generations}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use the formula for bacterial growth<\/h3>\n\n\n\n<p>The bacterial population after nn generations is given by: N=N0\u00d72nN = N_0 \\times 2^n<\/p>\n\n\n\n<p>Substitute the values: N=4\u00d723=4\u00d78=32N = 4 \\times 2^3 = 4 \\times 8 = 32<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Answer:<\/strong><\/h3>\n\n\n\n<p>After 90 minutes, the bacterial culture will contain <strong>32 bacteria<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>Bacteria reproduce through a process called binary fission, where one bacterial cell divides into two identical daughter cells. The time it takes for the bacterial population to double is known as the <strong>generation time<\/strong> or doubling time. In this case, the generation time is 30 minutes, meaning every 30 minutes the population doubles in size.<\/p>\n\n\n\n<p>Starting with 4 bacteria, after the first 30 minutes (one generation), the number of bacteria doubles from 4 to 8. After another 30 minutes (60 minutes total, or two generations), the population doubles again from 8 to 16. After a third 30-minute period (90 minutes total), it doubles once more from 16 to 32.<\/p>\n\n\n\n<p>Mathematically, the growth can be modeled using the exponential growth formula: N=N0\u00d72nN = N_0 \\times 2^n<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>N0N_0 is the initial number of bacteria,<\/li>\n\n\n\n<li>nn is the number of generations (total time divided by generation time),<\/li>\n\n\n\n<li>NN is the number of bacteria after nn generations.<\/li>\n<\/ul>\n\n\n\n<p>Because bacterial growth is exponential under ideal conditions (no nutrient limitations, no death), this model assumes all bacteria survive and divide at a constant rate.<\/p>\n\n\n\n<p>Hence, after 90 minutes, which encompasses 3 full generations, the bacterial population grows from 4 to 32 cells. This exponential increase illustrates why bacterial cultures can rapidly multiply, highlighting the importance of generation time in microbiology and medicine.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If a bacterial culture initially contains 4 bacteria and has a generation time of 30 minutes, how many bacteria will be present in the culture in 90 minutes? Assume that all bacteria survive. The correct answer and explanation is: Let&#8217;s break down the problem step-by-step: Problem: What is being asked? Find the total number of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-28663","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28663","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=28663"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28663\/revisions"}],"predecessor-version":[{"id":28667,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28663\/revisions\/28667"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28663"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28663"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}