Refresher - MATHEMATICS Quiz 8
PROBLEM 1:
In 1938, a federal law establishing a minimum wage was enacted, and
the wage was set at $0.25 per hour, the wage had risen to $5.15 per hour
by 1997. For a simple exponential function of the form y = abt that models
the federal minimum wage for 1938 – 1997, how many percent did the
wage increased per year from 1938 to 1997.
Solution:
y = ab t
when t = 0
0
0.25 = ab
a = 0.25
y = 0.25 b t
t = 1997 - 1938 = 59
y = 0.25 b 59
5.15 = 0.25 b 59
b = 1.0526
Federal minimum wage rose by 5.26% from 1938 to 1997.
, Refresher - MATHEMATICS Quiz 8
PROBLEM 2:
The function N = 0.4 x2 – 36x + 1000 approximates the number of accidents (N)
per 50 million miles for a driver who is x years old. The formula models reality for
16 ≤ x ≤ 74 (that is for drivers between 16 and 74 inclusively.
➀ What is the age of a driver predicted to have the least number of accidents
per 50 million miles driven?
➁ What is the least number of accidents?
Solution:
➀ Age of a driver predicted to have the least number of accidents per 50 million
miles driven
y = 0.4 x 2 - 36x + 1000
a = 0.4
b = - 36
c = 1000
b
x- (condition for min value of x)
2a
- (- 36)
x=
2(0.4)
x = 45 years old
➁ Least number of accidents
N = + 0.4 x 2 - 36x + 1000
N = +0.4(45)2 - 36(45) + 1000
N = 190
PROBLEM 1:
In 1938, a federal law establishing a minimum wage was enacted, and
the wage was set at $0.25 per hour, the wage had risen to $5.15 per hour
by 1997. For a simple exponential function of the form y = abt that models
the federal minimum wage for 1938 – 1997, how many percent did the
wage increased per year from 1938 to 1997.
Solution:
y = ab t
when t = 0
0
0.25 = ab
a = 0.25
y = 0.25 b t
t = 1997 - 1938 = 59
y = 0.25 b 59
5.15 = 0.25 b 59
b = 1.0526
Federal minimum wage rose by 5.26% from 1938 to 1997.
, Refresher - MATHEMATICS Quiz 8
PROBLEM 2:
The function N = 0.4 x2 – 36x + 1000 approximates the number of accidents (N)
per 50 million miles for a driver who is x years old. The formula models reality for
16 ≤ x ≤ 74 (that is for drivers between 16 and 74 inclusively.
➀ What is the age of a driver predicted to have the least number of accidents
per 50 million miles driven?
➁ What is the least number of accidents?
Solution:
➀ Age of a driver predicted to have the least number of accidents per 50 million
miles driven
y = 0.4 x 2 - 36x + 1000
a = 0.4
b = - 36
c = 1000
b
x- (condition for min value of x)
2a
- (- 36)
x=
2(0.4)
x = 45 years old
➁ Least number of accidents
N = + 0.4 x 2 - 36x + 1000
N = +0.4(45)2 - 36(45) + 1000
N = 190
