Question

The number of passengers using a railway fell from 190,205 to 174,989 during a 5-year period. Find the annual percentage decrease over this period.

Answer 1

Answer:

1.65%

Step-by-step explanation:

We will assume the percentage was the same over the 5 years. The number of passengers using a railway is expressed by the formula

                           $P(t) = P_{o}(1 - r)^{t}$

Where

P(t) is the number of passengers after 5 years

                  P(t) = 174,989

P₀ is the number of the passengers at the beginning of the period

                 P₀ = 190,205

r is the rate in percentage    r  = ?

t is time duration    t = 5 years

Substituting these given values into the formula,

                 $174,989 = 190,205(1 - r)^{5}$

                 $(1 - r)^{5} = \frac {174,989}{190,205}$

                 $1 - r = \sqrt[5]{ \frac {174,989}{190,205}}$

                 $1 - r = \sqrt[5]{0.920}$

                 $1 - r = 0.9835$

                 $r = 1 - 0.9835$

                 $r = 0.0165$

                r = 1.65%

The annual percentage decrease over the period of 5 years is 1.65%