1. Cell volume follows the discrete-time dynamical system v t +1=2.5 v t with an
ID: 2871772 • Letter: 1
Question
1. Cell volume follows the discrete-time dynamical system vt+1=2.5vt with an initial volume of 1450 m3 .
At what time will the volume reach 3350 m3?
2. The amount of C14 left t years after the death of an organism is given by Q(t)=Q0e0.000117t .
When will 0.1 of the original amount of C14 be left in the remains?
If 0.025 grams are present after 11000 years, how much C14 was oringinally present in the organism?
3. Consider the function S(t)=2e0.25t .
Is S(t) increasing or decreasing?
If the function is increasing, find the doubling time; if it is decreasing, Find the half-life.
Doubling Time or Half-Life:
For what value of t does S(t)=4.234?
Explanation / Answer
vt+1=2.5vt
vt+1/vt=2.5
v(0)=1450
v(t)=1450*2.5t
1450*2.5t =3350
2.5t =3350/1450
t=ln(3350/1450) /ln2.5
t=0.914
2) Q(t)=Q0e0.000117t .
Q0e0.000117t .=0.1Q0
e0.000117t .=0.1
0.000117t .=ln0.1
t=19680years
Q0e0.000117*11000 .=0.025
Q0=0.025/e0.000117*11000 .
Q0=0.0905gm initially present
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