# Homework Help: Age/weight relationship of female arctic foxes caught in Svalbard

1. Oct 23, 2005

### gillgill

The age/weight relationship of female arctic foxes caught in Svalbard, Norway, can be estimated by the function
M(t)=3102e^(-e)^(-0.022(t-56))
where t is the age of the fox in days and M(t) is the weight of fox in grams.
a) estimate the weight of a female fox that is 200 days old
i found that M(200)=2974.15g

b) Use M(t) to estimate the largest size that a female fox an attain (Hint: find lim as t->infinity M(t))

i found that it is 3102 grams

c)estimate the age of a female fox when it has reached 80% of its maximum weight.
is it
2481.6=3102e^(-e)^(-0.022(t-56))
0.8=e^(-e)^(-0.022(t-56))
then how do u solve for t?

d)estimate the rate of change in weight of an Arctic fox that is 200 days old.
how would u start this question?

2. Oct 23, 2005

### hypermorphism

That's a good approach. Use the natural logarithm function on both sides.
When you hear "rate of change of blah" you should immediately think of the derivative of blah.

3. Oct 23, 2005

### gillgill

0.8=e^(-e)^(-0.022(t-56))
ln0.8=e^(-.022(t-56)ln (-e)????
the power to the power is messing me up...

4. Oct 23, 2005

### hypermorphism

Just use the chain rule in a consistent manner. Pick an f(u) and a g(t) so that f(g(t)) = e^(-e)^(-0.022(t-56)), then apply the chain rule to (d/dt)(f(g(t)). For example, f(u) = e^u and g(t) = -e^(-0.022(t-56)).

5. Oct 23, 2005

### gillgill

does t=124.18?

6. Oct 24, 2005

### gillgill

for d)estimate the rate of change in weight of an Arctic fox that is 200 days old.
do u just find the deriviative of M(t)=3102e^(-e)^(-0.022(t-56))
and then sub in 200 after?

7. Oct 24, 2005

### HallsofIvy

Yes, of course. The "rate of change" is the derivative.