The population of a city is growing at an average rate of 3% per year in 1990 the population was 45 000.

1 answer:

5 0

This is an exponential growth/decay problem...

F=Ir^t, F=final value, I=initial value, r=rate, t=time, in this case:

F=I(1.03)^t and they just want to know when F=2I so

2=1.03^t take natural log of both sides...

ln2=t*ln1.03

t=ln2/(ln1.03)

t≈23.45

So it will take approximately 23.45 years for the population to double..

1990+23.45=2013.45

So during the year of 2013 the population will have double from its 1990 level.

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3 years ago

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Step-by-step explanation:

I'm not sure why you would need a table since the limit definition of a derivative (from what I'm remembering) gives you the exact formula anyway... so hopefully this at least helps point you in the right direction.

My work is in the attachment but I do want to address the elephant on the blackboard real quick.

You'll see that I got to the point where I isolated the h's and just stated the limit equaled the natural log of something out of nowhere. This is because, as far as I know, the way to show that is true is through the use of limits going to infinity. And I'm assuming that you haven't even begun to talk about infinite limits yet, so I'm gonna ask you to just trust that that is true. (Also the proof is a little long and could be a question on it's own tbh. There are actually other methods to take this derivative but they involve knowing other derivatives and that kinda spoils a question of this caliber.)