The population, P (t), in millions, of a country in year t,...

The population, P (t), in millions, of a country in year t, is given by the formula P (t) = 15 + 0.2t. (a) What is the country's initial population? The country's initial population is i million. (b) What is the average rate of change of the population in millions of people/year? Enter the exact answer. The average rate of change of the population is i million people/year.

Transcript

00:01 Okay, so in this question, it is given that the population of the china after t year is given by this equation.

00:07 And here we need to find the total change in population of china between 1 january 1993 to 2000.

00:20 Right? so first of all, here t, that is the number of year after 1993.

00:25 So for the year 1993, we can take t is equal to zero.

00:29 And for the year 2000, we can take t is equal to zero.

00:32 Equal to 7 right so first of all substitute t is equal to 0 in this equation 1 .0 1 .0 14 rest to 0 that is 1 .1 right so 1 multiply by 1 .15 that is 1 .15 now we need to substitute t is equal to 7 right and using the calculator we can find the value of p of 7 right so that is equal to approximately 1 .2675 right now let's say change in population that is dp right so it is given by p of 7 minus p of 0 now substitute both values over here right therefore dp is approximately equal to 0 .1175 and the unit will be billions of people so this is your answer number a now we need to find the average rate of change of population on this given period right so let's say average rate rate of change of population is m so m is given by dp divided by seven right because here 2000 minus 1993 that is equal to 7 dp is 0 .1175 and 7 will be as it is therefore approximate value of m is 0 .01679 and unit will be billion people per year right so this is the average rate of change of population and this is your answer number b right now our last question is is the average rate of change is greater or lesser than the instantaneous rate of change right so first of all to find the rate of change of population we need to take derivative of the given function with respect to time t 1 .1 5 is constant and derivative of 1 .014 is is 1 .014 to t multiply by log of 1 .014.

03:01 Right? and here we need to find the rate of change of population in 2000...

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