the size S of a tumor in mm cubed is given by S=2^t, where t is the number of months since the tumor was discovered a: what is the total change in the size of the tumor during the first 6 months?
and b: what is the average rate of change in the size of the tumor during the first 6 months?
and c: estimate the rate at which the tumor is growing at t=6?

Question

the size S of a tumor in mm cubed is given by S=2^t, where t is the number of months since the tumor was discovered a: what is the total change in the size of the tumor during the first 6 months?  
and b: what is the average rate of change in the size of the tumor during the first 6 months? 
and c: estimate the rate at which the tumor is growing at t=6?

anonymous · Answer

ick

anonymous · Answer

si!

anonymous · Answer

i got different answers than the book said so i am confused!

anonymous · Answer

at t = 0 it is 1
at t = 8 it is 
$$2^8=256$$

anonymous · Answer

oh it asked for t =6
 it is 
$$2^6=64$$

anonymous · Answer

so change in size is 
$$64-1=63$$ cubic mm

anonymous · Answer

average rate is 
$$\frac{63}{6}=10.5$$

anonymous · Answer

aha i forgot to subtract the one

anonymous · Answer

lol ok now right?  and instantaneous  rate at 6 is 
$$2^6\times \ln(2)$$

anonymous · Answer

how do you get the instantaneous rate?  that is where i keep getting stuck...the logical progression is at am impass because i don't follow how it works.

anonymous · Answer

i got it because i know the answer. if you do not you have to approximate with things like 
$$\frac{2^{6.1}-2^6}{.1}$$ and so on

anonymous · Answer

oh got ya! thanks

anonymous · Answer

yw