Group:
Name:
Math 137 - Calculus I for the Life Sciences
Tuesday, January 22
∗∗ Semilog and double-log plots
1. Suppose that x and y are related by the expression
y = 20 · 10− x/2 .
Find a linear relationship between x and log(y). Graph
the resulting relationship on the semilog plot to the right.
log10 (y) = log10 (20 · 10− x/2 ) = log10 (20) + log10 (10− x/2 ) = log10 (2) + 1 −
x
2
2. Given the semilog plot to the right, find a functional
relationship between x and y.
Let Y = log10 (y). We see that our graph contains the points (0, 50) and (2, 800), so we
obtain the equation
Y − log10 (50) =
log10 (800) − log10 (50)
( x − 0),
2−0
log10 (y) = Y = log10 (50) +
log10 (800/50)
x
2
hence
and
y = 10log10 (50)+log10 (16) x/2 = 10log10 (50) · 10log10 (16) x/2 = 50 · (10log10 (16) ) x/2 = 50 · 4x
3. Given the double-log plot to the right, find a functional
relationship between x and y.
Let Y = log10 (y) and X = log10 ( x ). We see that our graph contains the points (1, 5) and
(104 , 0.02). Then we obtain the equation
Y − log10 (5) =
log10 (5) − log10 (0.02)
( X − log10 (1)),
log10 (1) − log10 (104 )
hence
y = 10log10 (5)+
log10 (5/0.02)
−4
log10 ( x )
= 5 · x−
log10 (250)
4
4. Given the double-log plot to the right, find a functional
relationship between x and y.
Let Y = log10 (y) and X = log10 ( x ). We see that our graph contains the points (1, 0.1) and
(104 , 1). Then we obtain the equation
Y − log10 (0.1) =
hence
log10 (1) − log10 (0.1)
( X − log10 (1)),
log10 (104 ) − log10 (1)
1
y = 10log10 (0.1)+ 4 log10 ( x) = 0.1x1/4