Average Rate of Change

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Grimsuke

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Jan 7, 2017
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I have the question:
Suppose that number of residents, ?(?) (in hundreds) in a small community after t years is given by N(t) = 0.1t2 + 2t + 5.
I have to find the amount of initial residents but I have no idea of where to start. I tried looking in my textbook for a similar question but I didn't find anything. If you could give a hint about how to start, that would be amazing!
 
"Initial" means "at the start", which in turn means "after 0 years".

Does that suggest how to find the answer?
 
So that makes 0 = 0.1t2 + 2t + 5, right? Would I factor it? How would that work with 0.1?
 
N(t) = the number of residence of a community after t years. If N = 3 then there are 300 residence in the community.

N(t) = the number of residence after t years.
N(5) = the number of residence after 5 years.
N(7) = the number of residence after 7 years.

In the 3 lines above you do see that all that changed was the value of t.

When you solve N(t)=0 ,and you did by replacing N(t) with 0 in the equation 0 = 0.1t^2 + 2t + 5, you will find a t value corresponding to N(t) = 0. But you do NOT want to know when the population is 0. You want to know the population, which is a N value and not a t value, at the start. As you were told, at the start t=0. You wand to calculate N(0). Just replace the rhs with 0 for t and whatever you get will be equal to N(t).
 
Grimsuke said:
t=0? So N(t)=0.1(0)2 + 2(0) + 5 = 5?
Click to expand...
Correct. The initial number is N(0).

With experience, you'll be doing this part instantaneously on future problems!

Now, given the title you gave your question, there's more to the problem. If you need more help, show it to us along with whatever work you;ve tried (even if you know it's wrong).
 
Dr.Peterson said:
Correct. The initial number is N(0).

With experience, you'll be doing this part instantaneously on future problems!

Now, given the title you gave your question, there's more to the problem. If you need more help, show it to us along with whatever work you;ve tried (even if you know it's wrong).
Click to expand...
Thank you so much! I can't believe I have having such difficulties with it. It was so simple.
 
Can you please tell us the rest of the problem? Something about rate of change?
 
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