Rate of change of population after 2.5 hours?

Math Sucks
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Rate of change... derivative?

Homework Statement



the total number of people(in millions) present in a population at a given time is given by the function:

2t(5t+9)^1/2+12

where t represents time (in hours) find the rate in change of the population after 2.5 hours...

Homework Equations





The Attempt at a Solution



im so confused do i find the derivative ?
 
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Math Sucks said:

Homework Statement



the total number of people(in millions) present in a population at a given time is given by the function:

2t(5t+9)^1/2+12

where t represents time (in hours) find the rate in change of the population after 2.5 hours...

Homework Equations





The Attempt at a Solution



im so confused do i find the derivative ?

Sounds like a good idea to me. The derivative is the rate of change.
 


i got 10t+9..
 


10(2.5)+9... 34?
 


Math Sucks said:
i got 10t+9..

Now how did you get that? Your expression looks like 2 t \sqrt{5 t + 9}+12, is that right? Looks like you'll need the product rule and chain rule etc to differentiate it.
 
Last edited:
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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