Lesson 4 Common Sense Solidify Understanding

Ready

At the first of the year you opened a new bank account with a deposit of $$ 1,000$ . You don’t make another deposit or withdrawal during the year.

1.

Is there a difference between a bank account that earns $12 %$ interest paid once per year and one that pays $1 %$ interest every month? Why might they be the same? Why might they be different?

2.

Calculate the amount you will have in your account if you are paid $12 %$ interest once per year.

3.

Calculate the amount you will have in your account at the end of the year if you are paid $1 %$ interest at the end of each month.

At the first of the year you opened a new account with a deposit of $$ 13,000$ . You don’t make another deposit or withdrawal during the year.

4.

Calculate the amount you will have in your account, if it earns $8 %$ interest once per year.

5.

Calculate the amount you will have in your account at the end of the year, if your account earns $8 %$ interest per year, but it is calculated twice per year. (Note: The interest rate you use for your calculations at the end of $6 months$ will not be $8 %$ .)

6.

Calculate the amount you will have in your account at the end of the year, if your account earns $8 %$ interest per year, but it is calculated quarterly. (Note: The interest rate you use for your calculations at the end of $3 months$ will not be $8 %$ .)

Set

Evaluate the following logarithms.

7.

$\log 10$

8.

$\log 10^{- 7}$

9.

$\log 10^{75}$

10.

$\log 10^{x}$

11.

$\log_{3} 3^{5}$

12.

$\log_{8} 8^{- 3}$

13.

$\log_{11} 11^{37}$

14.

$\log_{m} m^{n}$

Solve each equation. Round answers to $3$ decimal places.

15.

$10^{n} = 4.305$

16.

$10^{n} = 0.386$

17.

$10^{n} = 14,521$

18.

$10^{n} = 483.059$

19.

$10^{3 n - 2} = 1,756$

20.

$3 (10^{n + 2}) = 32,721$

21.

$- 2 (10^{n - 5}) = - 8,619$

Go

The graphs of $f (x) = 10^{x}$ and $g (x) = \log x$ are shown in the same coordinate plane.

Make a list of the characteristics of each function.

22.

$f (x) = 10^{x}$

23.

$g (x) = \log x$

Each of the following problems refers to the graphs of the functions $f (x) = 10^{x}$ and $g (x) = \log x$ . State whether they are true or false. If they are false, correct the statement so that it is true.

24.

Every graph of the form $g (x) = \log x$ will contain the point $(1, 0)$ .

25.

Both graphs have vertical asymptotes.

26.

The graphs of $f (x)$ and $g (x)$ have the same rate of change.

27.

The functions are inverses of each other.

28.

The range of $f (x)$ is the domain of $g (x)$ .

29.

The graph of $g (x)$ will never reach $3$ .