1. ## calculus (urgent)

8.
ENDANGERED SPECIES An international agency studies an endangered tiger species for
Borneo. The population of the species is modeled by
N(t)=30+500e^(-0.3t)/1+5e^(-0.3t)

a. At what rate is the population changing at time
t? Will the population increase or
decrease?
b. When is the rate of change of the population increasing? When is it decreasing?

c. What happens to the population in the long run (
t→+∞)?

2. Originally Posted by cclia
8.
ENDANGERED SPECIES An international agency studies an endangered tiger species for
Borneo. The population of the species is modeled by
N(t)=30+500e^(-0.3t)/1+5e^(-0.3t)

a. At what rate is the population changing at time
[LEFT]t[FONT=TimesNewRoman]?
find N'(t), that's the rate
Will the population increase or
decrease?
if N'(t) > 0, then it is increasing, if N'(t) < 0, then it is decreasing

b. When is the rate of change of the population increasing? When is it decreasing?
again, find the intervals where the second derivative is positive or negative and state your finding accordingly. interpret your results means you describe the rate of change in words, which describes how the population is changing over certain intervals of time

c. What happens to the population in the long run (t→+∞)?
find $\displaystyle \lim_{t \to \infty} N(t)$

3. Originally Posted by cclia
8.

ENDANGERED SPECIES An international agency studies an endangered tiger species for

Borneo. The population of the species is modeled by
N(t)=30+500e^(-0.3t)/1+5e^(-0.3t)

a. At what rate is the population changing at time
t? Will the population increase or

decrease?

b. When is the rate of change of the population increasing? When is it decreasing?

c. What happens to the population in the long run (t→+∞)?
a. Calculate dN/dt. Is dN/dt positive or negative for t > 0 ....?

b. Calculate the derivative of dN/dt, that is, $\displaystyle \frac{d^2 N}{dt^2}$. For what values of t is $\displaystyle \frac{d^2 N}{dt^2}$ greater than zero and less than zero ....?

c. Consider the limit $\displaystyle \lim_{t \rightarrow + \infty} \frac{30 + 500 e^{-0.3t}}{1 + 5 e^{-0.3t}} \, ....$

(I assume that's your expression for N - what you've posted is quite ambiguous)

And you know $\displaystyle e^{-0.3 t} \rightarrow 0$, right .....?