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# Exponential growth and decay

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The number of rabbits, R in a population after M months is modelled by the formula

R = 12e^(0.2m)

Show that after 6 months the rabbits population is increasing by almost 8 rabbits per month

so for this one i assumed my initial value before the 6 months would be 12

then i made m= 6 which gave me the answer of 39.8, rounded to the nearest whole number = 40

40- 12= 28, the amount increased during the 6 months period

28/6 = 4.6

this is where i noticed i went completely wrong, please explain as i am quite new to this topic thank you

Feb 7, 2019

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All pretty good, except this is an EXPONENTIAL function....it is not linear month-to-month but is INRASING each month

(I am assuming you do NOT know how to derive   dm/dt   the rate function of this population function)

month 5 = 32.62

month 6 = 39.84

month 7 =  48.66

A little 'narrower' range of months ( rahter than 0 - 6 months) will yield better 'average'

in two months from 5 to 7       (48.66-32.62 ) / 2 = 8.02 rabits per month increase

or from month 5 to month 6   =  39.84 - 32.62  = 7.22 rabbits/month

Let's look at month  5.5 to 6.5  =  44.03   -36.05= 7.98 rabbits/month

Feb 7, 2019
edited by ElectricPavlov  Feb 7, 2019
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ok i will do some researches about that,

thanks for the detailed explanation

YEEEEEET  Feb 7, 2019