Question 1

Solve the problem.
-Assume that a savings account earns interest at the rate of 2% compounded monthly. If this account contains $1000 now, how many months will it take for this amount to double if no withdrawals are made?
A) 417 months
B) 12 months
C) 450 months
D) 408 months

Accepted Answer

The amount of money in the account after t months is given by the formula A = 1000(1 + 0.02/12)^12t. We want to find t such that A = 2000. Solving for t, we get t = 417.

Question 2

Solve the problem.
-U. S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x) = 51.42 + 15.473 · log x , where x = 0 is 1980. How many families were there in 2002?
A) 48 million
B) 72 million
C) 21 million
D) 90 million

Accepted Answer

To find the number of families in 2002, we need to substitute x = 22 (since 2002 is 22 years after 1980) into the formula:
h(22) = 51.42 + 15.473 · log 22
≈ 72 million
Therefore, the answer is B: 72 million.

Question 3

Solve the problem.
-The level of a sound in decibels (db) is determined by the formula N = 10 · log(I × 1012) db, where I is the intensity of the sound in watts per square meter. A certain noise has an intensity of 8.49 × 10-4 watts per square
Meter. What is the sound level of this noise? (Round your answer to the nearest decibel.)
A) 89 db
B) 206 db
C) 79 db
D) 9 db

Accepted Answer

Using the formula N = 10 · log(I × 10^12) db and substituting I = 8.49 × 10^-4, we get N = 10 · log(8.49 × 10^-4 × 10^12) = 10 · log(8.49 × 10^8). Calculating this gives a value close to 89 db when rounded to the nearest decibel.

Question 4

Solve the problem.
-Book sales on the Internet (in billions of dollars) in year x are approximated by f(x) = 1.84 + 2.1 · ln x, where x = 0 corresponds to 2000. How much will be spent on Internet book sales in 2008? Round to the nearest tenth.
A) 6.2 billion
B) 6.0 billion
C) 3.9 billion
D) 8.0 billion

Accepted Answer

To find the sales in 2008, we substitute x = 8 (since x = 0 corresponds to 2000, x = 8 corresponds to 2008) into the given function: f(x) = 1.84 + 2.1 · ln x. Therefore, f(8) = 1.84 + 2.1 · ln(8). Calculating this gives approximately 6.2 billion dollars.

Quiz 1: Functions and Graphs

Solve the problem. -Assume that a savings account earns interest at the rate of 2% compounded monthly. If this account contains $1000 now, how many months will it take for this amount to double if no withdrawals are made?

Solve the problem. -U. S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x) = 51.42 + 15.473 · log x , where x = 0 is 1980. How many families were there in 2002?

Solve the problem. -Book sales on the Internet (in billions of dollars) in year x are approximated by f(x) = 1.84 + 2.1 · ln x, where x = 0 corresponds to 2000. How much will be spent on Internet book sales in 2008? Round to the nearest tenth.