Age/weight relationship of female arctic foxes caught in Svalbard

[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?

 

[hypermorphism]

...
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?

That's a good approach. Use the natural logarithm function on both sides.

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

When you hear "rate of change of blah" you should immediately think of the derivative of blah.

 

[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...

 

[hypermorphism]

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...

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)).

 

[gillgill]

does t=124.18?

 

[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?

 

[HallsofIvy]

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