Math 112 Quiz
Problem 1 (3 points): Solve for x:
ex= 42x+152
Solution: Take ln of both sides to get:
x= (2x+ 1) ln(4) + 2ln(5)
x[1 โ2 ln(4)] = ln(4) + 2 ln(5)
x=ln(4) + 2 ln(5)
1โ2 ln(4)
Problem 2 (2 points): Plutonium has a half-life of 25,000 years. Suppose you have
a 10g sample. How much will be left after 75,000 years?
Solution:
After 25,000 years: (10g)(.5)=5g left
After 50,000 years: (5g)(.5)=2.5g left
After 75,000 years: (2.5g)(.5)=1.25g left
Problem 3 (2 points): Simplify โ2+i
1โi.
Solution:
โ2 + i
1โi=(โ2 + i)(1 + i)
(1 โi)(1 + i)=
โ3โi
2
Problem 4 (3 points): Consider the polynomial f(x) = x3+ 2x2+x+ 2. The
remainder when f(x)is divided by (x+ 2) is 0. Find all the roots of f(x).
Solution: (x+2) is a factor means -2 is a root.
f(x)/(x+ 2) = x2+ 1
so the other roots are +i and -i.