SOLUTION: Please help me answer this question: The number N of tourists visiting a city in the t-th year after 2010 can be represented by the following formula: N = 114000 + 100

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Question 1154750: Please help me answer this question:
The number N of tourists visiting a city in the t-th year after 2010 can be represented by the following formula:
N = 114000 + 100000log(t+1)
It is given that the number of tourists in the t-th year is increased by 8000 when compared with that in the previous year.
(a) Will the number of tourists visiting the city per year be more than 214000 after 2019?

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula is N = 114000 + 100000 * log(T + 1)
T is equal to 0 in the year 2010.
T is equal to 9 in the year 2019.
you want to know if the number of tourists visiting the city per year will be greater than 214000 after 2019.
the formula for year 2019 is:
N = 114000 + 100000 * log(9 + 1).
simplify to get:
N = 114000 + 100000 * log(10).
solve for N to get:
N = 214000.
the formula for year 2020 is:
N = 114000 + 100000 * log(10 + 1)
simplify to get:
N = 114000 + 100000 * log(11)
solve for N to get:
N = 218139.2685
that is greater than 214000, so the answer to question (a) is yes.
the fly in the ointment her is the statement that it is given that the number of tourists in the year represent by t is 8000 when compared with that in the previous year.
this is not true because the formula is not linear and therefore the increase in the number of tourists each year will not be the same.
i graphed the equation by making N = y and T = x.
you can see from the graph that the increase in the number of tourists between 2019 and 2020 is not 8000.
the graph is shown below.
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