
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 24th, 2015, 09:12 PM  #1 
Newbie Joined: Oct 2015 From: Canada Posts: 5 Thanks: 0  Derivatives, trignometric functions and exponential functions
Hey guys I need help with few questions they are: 1 A dinosaur bone from an archaeological site has onefifth of the amount of Carbon 14 than it originally contained. Determine the approximate age of the bone given that Carbon 14 has a half life of 5770 years. 2 The number of people in a small town became zombies after t days during a zombie apocalypse is given by N(t) and is approximated by the exponential model N(t) =10000/1 + 12.5e^kt If 80 people are zombies by the day 10 , find how many people become zombies by day 15. Thanks 
November 24th, 2015, 10:27 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,236 Thanks: 2412 Math Focus: Mainly analysis and algebra 
$c(t) = A\mathrm e^{kt}$ and $c(5770)=\frac12c(0)$. So $$\begin{aligned} A\mathrm e^{5770k} &= \frac12A \\5770k &= \log \frac12 \\ k &= {\log 2 \over 5770} \end{aligned}$$ Then we have $c(0) = \frac15 c(T)$ so$$\begin{aligned} A &= \frac15A\mathrm e^{{\log 2 \over 5770}T} \\ \log 5 &= {\log 2 \over 5770}T \\ T &= {5770\log 5 \over \log 2} \\ &= 13397.5 = 13400 \text{ years} \end{aligned}$$ I think there's something wrong with question 2. 
November 25th, 2015, 06:20 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,970 Thanks: 807  Quote:
Quote:
Quote:
Solve that for k. Start by dividing both sides by 12.5 then take the logarithm of both sides. (Since the number of zombies is increasing, k will be negative.) Quote:
$\displaystyle \frac{10000}{1+ 12.5e^{kt}}$ Quote:
 

Tags 
derivatives, exponential, functions, trignometric 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
derivatives of exponential functions  pomazebog  Calculus  2  March 5th, 2012 08:23 AM 
Derivatives of exponential and log functions review help!  ProJO  Calculus  4  March 6th, 2011 09:49 AM 
Derivatives of trigonometric functions  TsAmE  Calculus  10  April 23rd, 2010 01:33 AM 
functions and their derivatives  waytogo  Algebra  4  January 12th, 2010 09:24 PM 
Functions, Derivatives...Help me please?  lilxswttooth  Calculus  1  September 21st, 2009 04:50 AM 