A town has the population 9000 people at year t=0. write a formula a. The population shrinks by 60 people per year b. the populcaiton shrinks by 8% per year c. The population shrinks at a continuous rate of 8% per year
A town has the population 9000 people at year t=0. write a formula
a. The population shrinks by 60 people per year
b. the populcaiton shrinks by 8% per year
c. The population shrinks at a continuous rate of 8% per year
A town has the population 9000 people at year t=0. write a formula
let a=9000,
t=0,
Let t1 is the population of town after one year.
a. The population shrinks by 60 people per year.
We know that A.M. formula,
tn=a+(n-1)d
Where 'a' is initial value, here a=9000.
Population at first year t1=9000-60=8940
d is common difference, here d=-60.
Therefore
tn=t1 +(n-1)(-60).
tn=8940-60n+60
tn=9000-60n.
b. the population shrinks by 8% per year.
We know that
Where tn is the population at nth year.
r is rate of interest, here r=-8%,
P is initial population, Here P=9000,
Therefore
c. The population shrinks at a continuous rate of 8% per year.
We know that
Where A is population of town at nth year,
P is initial population, here P=9000.
and r is rate , here r=-8%=-0.08
n is time in year.
Therefore
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