Answer:
[tex]P=3000(0.89)^t[/tex]
Step-by-step explanation:
It was given that, florida manatee population is 3,000 and is decreasing by 11% each year.
We want to write a function for this situation.
Since the population is decreasing annually, it is modelled by:
[tex]P=P_0(1-r\%)^t[/tex]
We substitute the give initial population and rate of decrease to get:
[tex]P=3000(1-0.11)^t[/tex]
This simplifies to:
[tex]P=3000(0.89)^t[/tex]
Answer:[tex]P_{(t)}=P_{o}(1-0.11)^{t}[/tex]
Step-by-step explanation:
According to the described situation, the current manatee population is 3000, if it decreases [tex]11\%=0.11[/tex] each year this means in one year the manatee population will be:
[tex]3000-(3000(0.11))=2671[/tex] (1)
And the next year:
[tex]2671-(2671(0.11))=2376.3[/tex] (2)
This mean each year the population will be [tex]11\%[/tex] less than last year.
So, in this case we can use the following function to express this decrease:
[tex]P_{(t)}=P_{o}(1+r)^{t}[/tex] (3)
Where:
[tex]P_{(t)}[/tex] Is the number of manaties at time [tex]t[/tex]
[tex]P_{o}=3000[/tex] is the current number of manaties (this year)
[tex]r=-11\%=-0.11[/tex] is the decrease rate of the population
[tex]t[/tex] is the time (in years)
For example, if we want to estimate the number of manaties for next year, [tex]t=1[/tex]:
[tex]P_{(1)}=3000(1-0.11)^{1}[/tex]
[tex]P_{(1)}=2670[/tex]
If we want to estimate the number of manaties in two yeas, [tex]t=2[/tex]:
[tex]P_{(2)}=3000(1-0.11)^{2}[/tex]
[tex]P_{(2)}=2376.3[/tex]
