Answered: Starting in 1983 the number of visitors…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Starting in 1983 the number of visitors (in thousands) to a park has decreased by 9.6 thousands people every four years. In addition, records show that in 1987 there were 83.8 thousand visitors to the park. If the current trend continues when will the number of visitors be 55.9 thousand people?

Expert Solution

Step 1

Given data:

The number of visitors to a park decreased by 9.6 thousand people every 4 years starting from 1983
In 1987, number of visitors to the park=83.8 thousand

Thus, number of visitors in the year 1983 $= (83.8 + 9.6)$ thousand

$= 93.4$ thousand

This is a problem of arithmetic progressions with first term, $a = 93.4$

Common difference, $d = - 9.6$

Last term, $a_{n} = 55.9$

The formula for n is given by:

$a_{n} = a + (n - 1) d$

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