My Math Forum find instantaneous rate of change

 Pre-Calculus Pre-Calculus Math Forum

 January 10th, 2016, 10:44 AM #1 Newbie   Joined: Feb 2015 From: canada Posts: 10 Thanks: 0 find instantaneous rate of change for 500g of a radioactive substance with a half-life of 5.2 h, the amount remaining is given by the formula M(t) = 500(0.5)^t/5.2 where M is mass remaining and t is in hours. Estimate the instantaneous rate of change in mass at 1 day. I keep getting -2 as the answer. The answer in the book is -0.111. Can someone please show me how to do this? I have no idea what I'm doing wrong.
 January 10th, 2016, 01:21 PM #2 Global Moderator   Joined: May 2007 Posts: 6,770 Thanks: 700 I suggest you show us how you did it.
February 23rd, 2016, 04:54 AM   #3
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Quote:
 Originally Posted by rrosa522 for 500g of a radioactive substance with a half-life of 5.2 h, the amount remaining is given by the formula M(t) = 500(0.5)^t/5.2
You mean M(t)= 500(0.5)^(t/5.2)= $\displaystyle 500(0.5)^{t/5.2}$. What you wrote is $\displaystyle 500\frac{0.5^t}{5.2}$

Quote:
 where M is mass remaining and t is in hours. Estimate the instantaneous rate of change in mass at 1 day. I keep getting -2 as the answer. The answer in the book is -0.111. Can someone please show me how to do this? I have no idea what I'm doing wrong.
What did you do? Did you differentiate the function? If so what did you get for the derivative?

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### rate of change in mass half life

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