Question 1200292
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The population of a town grows at a rate of  e^1.2t-2t  people per year (where t is the number of years). 
At   t=2   years, the town has  1500  people. Approximately by how many people do the population grow 
between  t=2  and  t=5? What is the town’s population at  t=5  year? 
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My personal opinion is that this problem is worded and posed incorrectly.


More concretely, it is a soup of words, that are used incorrectly.



It is why I did not touch it and do not want to touch it.



<pre>
    If to read it literally, then it requires to solve a differential equation


        {{{(dp)/(dt)}}} = {{{e^(1.2t) - 2t}}},


    where "p" is the population.



    But in this case,  the expression  {{{e^(1.2t) - 2t}}}  is not  " the rate per year " : it is  <U>simply</U>  " the rate "

    or, if to be precisely accurate, " the instantaneous rate ".
</pre>