algebra quiz help

Quiz 6 - SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

University of Maryland University College

SPRING 2016, MATH 107

Quiz 6

Prof. Minhtri Ho

Problem 1:

Use the properties of logarithms to write the following as a single logarithm. Simplify

your answer:

log3(x 3 − 1) − log3(x

2 + x + 1)

Problem 2:

Use an appropriate change of base formula to convert the following expression to the

indicated base:

10x to base e

Problem 3: Give a numerical example to show that, in general:

logb(xy) 6= logb(x) logb(y)

Problem 4:

Solve the following equation:

45x = 161−2x

Problem 5:

Solve the following inequality:

2x 2−4x − 32 ≥ 0

SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

Quiz 6 - SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

Problem 6:

Find the formula for its inverse function1:

f(x) = ex

ex + 1

Problem 7:

Find the formula for its inverse function2:

f(x) = 2 ln(x)

1 − ln(x)

Problem 8:

Solve the following equation:

log2(x + 3) = log2(5 −x) + 4

Problem 9:

Suppose $4000 is invested in an account which offers 6.25% compounded monthly.

a) Express the amount A in the account as a function of the term of the investment t in

years

b) How much is in the account after 4 years?

c) How long will it take for the initial investment to double?

1The given function is one-to-one; you do not have to check for it 2The given function is one-to-one; you do not have to check for it

SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

Quiz 6 - SPRING 2016 - MATH 107 - COLLEGE ALGEBRA

Problem 10:

A 40◦F roast is cooked in a 400◦F oven. After 2.5 hours, the temperature of the roast is

150◦ F.

a) Assuming the temperature of the roast follows Newton’s Law of Warming, find a for-

mula for the temperature of the roast T as a function of its time in the oven, t, in

hours.

b) The roast is done when the internal temperature reaches 170◦F. When will the roast

be done?

SPRING 2016 - MATH 107 - COLLEGE ALGEBRA