# Calculus

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1. In a certain country, the percentage of the population relocating to a new town is given by the following function:

p(t) = 20.6e^-0,009t,where 0 ¡Ü t ¡Ü 52.

Time is zero (t = 0) corresponds to the year 1960.

1. Find the rate at which people relocated during the year of your birth.

2. Find the relocation rate of today.

What does this tell you about the country¡¯s population? Is there a peak (max) relocation year? Do you think this model is appropriate for predicting population movement? Share and compare calculations with another classmate

• Calculus -

p ' (t) = (-.009)(20.6) e^(-.009t)

plug in your birth-year. Sorry, I don't know it, you didn't invite me to your birthday party.

"today" ---> t = 53 , which is beyond the domain given. (Time to get a new edition of the textbook)

if you want to do it anyway
p ' (53) = (-.009)(20.6) e^(-.009(53) )
= appr -.115

max relocation ----> set p ' (t) = 0
(-.009)(20.6) e^(-.009t) = 0
e^(-.009t) = 0
no solution, thus no max

• Calculus -

p'(53) = (-.009)(20.6)e^(-.009(53))
= -.1854e^((-.477)
= -.1854 * .62064
= -.115067
= -.115067 * 100
= -11.5067 % change in
relocation rate