Question

A certain species of alligators is to be introducers into a swamp, and wildlife experts estimate the population will grow to P(t)=(803)3^t/3, where t represents the number of years from the time of introduction. what is the tripling time for this population of alligators

Answer 1

Answer:

3 years

Step-by-step explanation:

Note that:

P(0) = 803

So Tripling time  ==>  P(t) = 3*P(0) = 3*803 = 2409

Then we have an equation:

2409  = 803*$3^{\frac{t}{3} }$

<=> 3 = $3^{\frac{t}{3} }$  

<=> 1 = $\frac{t}{3}$

<=> t = $3$

So the tripling time for this population of alligators is 3 years

Answer 2

Answer:

3 years

Step-by-step explanation:

[TeX] P(t)=803 X 3^{t/3}[/TeX]

First, we determine the initial population.

At t=0

[TeX] P(0)=803 X 3^{0/3}[/TeX]

P(0)=803

For the initial population to triple.

P(t)=3P(0) = 3 X 803 = 2409

[TeX] P(t)=803 X 3^{t/3}[/TeX]

[TeX] 2409=803 X 3^{t/3}[/TeX]

[TeX] \frac{2409}{803}= 3^{t/3}[/TeX]

[TeX] 3= 3^{t/3}[/TeX]

Since the bases are equal

[TeX] \frac{t}{3}=1[/TeX]

t=3

In 3 years, the population of the alligators will be triple its population at introduction.