Question

The florida manatee population is 3,000 and is decreasing by 11% each year. Write a function for this situation.

Answer 1

Answer:

$P=3000(0.89)^t$

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:

$P=P_0(1-r\%)^t$

We substitute the give initial population and rate of decrease to get:

$P=3000(1-0.11)^t$

This simplifies to:

$P=3000(0.89)^t$

Answer 2

Answer:$P_{(t)}=P_{o}(1-0.11)^{t}$

Step-by-step explanation:

According to the described situation, the current manatee population is 3000, if it decreases $11\%=0.11$ each year this means in one year the manatee population will be:

$3000-(3000(0.11))=2671$ (1)

And the next year:

$2671-(2671(0.11))=2376.3$ (2)

This mean each year the population will be $11\%$ less than last year.

So, in this case we can use the following function to express this decrease:

$P_{(t)}=P_{o}(1+r)^{t}$ (3)

Where:

$P_{(t)}$ Is the number of manaties at time $t$

$P_{o}=3000$ is the current number of manaties (this year)

$r=-11\%=-0.11$ is the decrease rate of the population

$t$ is the time (in years)

For example, if we want to estimate the number of manaties for next year, $t=1$:

$P_{(1)}=3000(1-0.11)^{1}$

$P_{(1)}=2670$

If we want to estimate the number of manaties in two yeas, $t=2$:

$P_{(2)}=3000(1-0.11)^{2}$

$P_{(2)}=2376.3$