The graph of P=f(t) to the right gives the population of a...

The graph of P=f(t) to the right gives the population of a town, in thousands, after t years. (a) Find the average rate of change of the population of the town during the first 20 years Average rate of change= 0.8 people per year. (b) Does the population of the town grow more between t = 5 and t = 10 or between t = 15 and t = 30? The population grows more between t = 5 and t = 10. (c) Does the population of the town grow faster between t = 5 and t = 10 years, or between t = 15 and t = 30 years? The population grows faster between t = 5 and t = 10

Transcript

00:01 Hi, there is a question that find the average rate of change of the population of the town during the first 20 years and in graph population is being given as a function of time and the population age in thousands after t years okay, first is okay, so now i need to just like this so p equal to f t okay, it is being already given now i have to find the average rate of change in the population of the town during first time during first time 20 years so first 20 years average rate of change that would be population after 20 years population in the starting divided by 20 minus 0 so at 20 years this is 20 years so population this must be 25 so 22 .5 approximately i can take this this must be 1 2 3 let us say 22 minus f0 a 5 divided by 20 so 17 by 20 17 by 20 which is 0 .8 5 people per year second question second part of the question says does the population of the town grow more between t equal to 5 and t equal to 10 or between 15 to 30 so between t equal to 5 to t equal to 10 so population after t equal to 10 is 12 .5 and minus population t equal to five this is five that would be 7 .5 7 .5 so 5 thousand people and between t equal to 15 to t equal to 13 30 t equal to 15 it is like here this is 15 16 17 18 so t equal to at 15 this is 18 and t equal to 30 it is 25 so 25 minus 18 which is 7 that means between t equal to 15 and t 30 the population and grows more this should be the answer for this part c does the population of the town grows faster between t equal to 5 t equal to 10 or between 2 2 equal to 15 to t equal to 30 so i need to find rate rate between t equal to 5 to t equal to 10 t equal to 5 to t equal to 10 that will be f 10 minus f5 divided by 10 5.

03:24 So we have to calculate f10 which is 12 .5 minus 7 .5.

03:29 This is 5 divided by 5 which is 1.

03:34 And between t equal to 15 and t equal to 30, average will be f 30 minus 15 by 30 minus 15.

03:50 So this is 7.

03:52 The numerator will be 7 minus 15.

03:54 7.

03:54 7 minus 15...

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