Deck 4: Living in a Nonlinear World

Question 1

Find the simple interest and the total amount including interest. $$\begin{array} { c | c | c | c | c } \text { Principal } & \text { Annual Interest Rate } & \text { Time in Years } & \text { Interest } & \text { Total Amount } \\\hline \$ 6000 & 6 \% & 2 & &\end{array}$$

Answer 1

$720; $6720

Question 2

Write the equation in the form $a x ^ { 2 } + b x + c = 0$
Then identify the values of a, b , and c .
-9 x(8 x+9)=4 x

Answer 2

$$- 72 x ^ { 2 } - 85 x + 0 = 0 ; a = - 72 , b = - 85 , c = 0$$

Question 3

Graph the function $f ( x ) = 2 ^ { x }$ .
Plot at least three points.

Answer 3

Question 4

$30,000 is invested in an account that pays 2% simple interest. If the money is invested for 10 years, how much will the account be worth?

Question 5

Solve the equation by using the quadratic formula. $$3 x ^ { 2 } + 15 x - 72 = 0$$

Question 6

Factor the binomial completely. $$t ^ { 2 } - 9$$

Question 7

Multiply the conjugates. $$\left( \frac { 11 } { 2 } x + \frac { 2 } { 5 } \right) \left( \frac { 11 } { 2 } x - \frac { 2 } { 5 } \right)$$

Question 8

For $f ( x ) = 2 ^ { x }$ , find for $f ( 1 ) \text { and } f ( - 3 ) \text {. }$

Question 9

Solve the equation by using the quadratic formula. $$x ^ { 2 } + 7 x - 8 = 0$$

Question 10

Josephine deposited $8,000 in an account that pays 6% compounded annually.
Complete the table to determine the amount of her investment at the end of 3
years. $$\begin{array} { l | l | l } \text { Year } & \text { Interest } & \text { Total } \\\hline \text { 1st } & & \\\text { 2nd } & & \\\text { 3rd } & &\end{array}$$

Question 11

Find the difference of
$\left( 4 m ^ { 3 } - 2 m + 24 \right) \text { and } \left( - 11 m ^ { 3 } + m ^ { 2 } + 16 m \right)$

Question 12

Add the polynomials. $$\left( \frac { 7 } { 2 } y ^ { 3 } + 2 y - \frac { 1 } { 4 } \right) + \left( 2 y ^ { 3 } - 4 y ^ { 2 } + \frac { 21 } { 2 } \right)$$

Question 13

Subtract the polynomials. $$\left( \frac { 15 } { 2 } y ^ { 3 } + 2 y - \frac { 1 } { 4 } \right) - \left( 2 y ^ { 3 } - 8 y ^ { 2 } + \frac { 27 } { 2 } \right)$$

Question 14

Factor completely. $$a ^ { 2 } + 3 a b - 8 b ^ { 2 }$$

Question 15

Write the equation in the form $a x ^ { 2 } + b x + c = 0$ Then identify the values of a, b , and c .
$- 4 x ^ { 2 } + x = 3$

Question 16

Subtract the polynomials. $$\left( 4 t ^ { 3 } - 12 t + 6 \right) - \left( - 6 t ^ { 3 } + t ^ { 2 } + 16 t \right)$$

Question 17

Factor completely. $$m ^ { 2 } + 4 m - 96$$

Question 18

Simplify the expression. Write the answer in exponent form. $$y ^ { 3 } \cdot y ^ { 5 } \cdot y ^ { 7 } \cdot y ^ { 9 }$$

Question 19

Simplify the expression. Write the answer in exponent form. $$10 ^ { 5 } \cdot 10 ^ { 7 }$$

Question 20

Solve the equation. $$4 ^ { y } = 64$$

Question 21

Add the polynomials. $$\left( 4 w ^ { 2 } + 8 w \right) + \left( 3 z ^ { 2 } - 5 z \right)$$

Question 22

Scientists often use a process called carbon dating to estimate the age of
archaeological finds. The process measures the amount of carbon-14, a
radioactive isotope with a half-life of 5730 years. If a sample of wood from an
ancient artifact had 19 grams of carbon-14 initially, the amount remaining, in grams,
is given by $$A ( t ) = 19 \left( \frac { 1 } { 2 } \right) ^ { t / 5730 }$$
where $t$ is the number of years since the tree died. How many grams would be present after 22,920 years?

Question 23

Find the opposite of the polynomial. $$- 9 x ^ { 4 } + 16 x ^ { 2 } - 11$$

Question 24

Factor completely. $$t ^ { 2 } + 10 t + 16$$

Question 25

Factor completely. $$x ^ { 2 } + 10 x y + 25 y ^ { 2 }$$

Question 26

Graph the function $f ( x ) = 3 ^ { x + 2 }$ .
Plot at least three points.

Question 27

Find the total amount for the investment using compound interest. $$\begin{array} { c | c | c | c | c } \text { Principal } & \text { Annual Interest Rate } & \text { Time in Years } & \text { Compounded } & \text { Total Amount } \\\hline \$ 9000 & 8.5 \% & 5 & \text { annually } &\end{array}$$

Question 28

Find all values of k so that the distance from (8, -5)to (11, k)is 5 units.

Question 29

Factor completely. $$x ^ { 2 } - 15 x + 54$$

Question 30

Nick borrowed $2000 for 4 years and 3 months at 8% simple interest.
a. How much interest will Nick have to pay?
b. What will be the total amount that he has to pay back?

Question 31

Write the equation in the form $a x ^ { 2 } + b x + c = 0$
Then identify the values of a, b , and c .
$x ^ { 2 } + 36 = 0$

Question 32

Simplify the expression. Write the answer in exponent form. $$y ^ { 3 } \cdot y ^ { 5 } \cdot y ^ { 7 } \cdot y ^ { 9 }$$

Question 33

Write the number in scientific notation.
483,000,000

Question 34

Carla deposited $12,400 into an account paying 4% simple interest 5 years ago.
If she withdraws the entire amount of money, how much will she have?

Question 35

Find the length of the unknown side.

Question 36

Factor the binomial completely. $$16 x ^ { 2 } + 9 y ^ { 2 }$$

Question 37

Graph the function $f ( x ) = 2 ^ { x }$ .
Plot at least three points.

Question 38

Write the distance formula.

Question 39

In a right triangle, one leg measures 14 km and the other leg measures 48 km.
Find the length of the hypotenuse.

Question 40

If $6000 is invested in an account that pays 9% interest compounded monthly
for 4 years, label the variables P, r, n, and t.

Question 41

Simplify.

Question 42

Simplify. Write your answer in exponent form.

Question 43

Write the number in scientific notation.

Question 44

Find the simple interest and the total amount including interest. $$\begin{array} { c | c | c | c | c } \text { Principal } & \text { Annual Interest Rate } & \text { Time in Years } & \text { Interest } & \text { Total Amount } \\\hline \$ 5000 & 5.2 \% & 5 & &\end{array}$$

Question 45

Multiply the conjugates.

Question 46

Factor the binomial completely. $$25 x ^ { 2 } - 81 y ^ { 2 }$$

A) $( 5 x + 9 y ) ^ { 2 }$
B) $( 5 x - 9 y ) ^ { 2 }$
C) $( 5 x + 9 y ) ( 5 x - 9 y )$
D) $( 25 x + 9 y ) ( x - 9 y )$

Question 47

Factor the polynomial completely.
$x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144$

A) The polynomial is prime.
B) $( x - 4 ) ^ { 2 } ( y - 3 ) ^ { 2 }$
C) (x y-16)(x y-9)
D) (x-4)(x+4)(y-3)(y+3)

Question 48

Factor the binomial completely. $$5 n ^ { 2 } - 80$$

Question 49

Find the vertex of the parabola.

Question 50

Perform the indicated operations. $$\left( 19 t ^ { 4 } - 2 t ^ { 2 } + 4 t \right) + \left( 2 t ^ { 4 } - 4 t + 27 \right) - \left( 4 t ^ { 4 } + t ^ { 2 } + 19 \right)$$

A) $16 t ^ { 4 } + 8$
B) $17 t ^ { 4 } - 3 t ^ { 2 } + 8$
C) $21 t ^ { 4 } - 3 t ^ { 2 } + 8 t - 8$
D) $25 t ^ { 4 } - 3 t ^ { 2 } + 46$

Question 51

Simplify.

Question 52

Factor completely.
$t ^ { 4 } x ^ { 2 } - 6 t ^ { 3 } x ^ { 3 } + 9 t ^ { 2 } x ^ { 4 }$

A) $\left( t ^ { 2 } - 3 x ^ { 2 } \right) ^ { 2 }$
B) $\left( t ^ { 2 } + 9 x ^ { 2 } \right) ^ { 2 }$
C) $t ^ { 2 } x ^ { 2 } ( t - 3 x ) ^ { 2 }$
D) $t ^ { 2 } x ^ { 2 } ( t + 9 x ) ^ { 2 }$

Question 53

Clear parentheses and combine like terms.

Question 54

Scientists often use a process called carbon dating to estimate the age of archaeological finds. The process measures the amount of carbon-14, a radioactive isotope with a half-life of 5,730 years. If a sample of wood from an ancient artifact had 15 grams of carbon- 14 initially, the amount remaining, in grams, is given by

where t is the number of years since the tree died. How many grams would be present after 5,730 years?

A) 30 g
B) 0.27 g
C) 7.5 g
D) 3.75 g

Question 55

The amount of $6,000 is invested at 5% for 3 years.
a. Compute the ending balance if the bank calculates simple interest.
b. Compute the ending balance if the bank calculates interest compounded annually.
c. How much more interest is earned in the account with compound interest?

Question 56

If a bank compounds interest quarterly for 10 years, how many total compound periods are there?

A)There are 60 total compound periods.
B)There are 5 total compound periods.
C)There are 20 total compound periods.
D)There are 40 total compound periods.

Question 57

Simplify the expression. Write the answer in exponent form. $$7 ^ { 5 } \cdot 7 ^ { 7 }$$

Question 58

If a bank compounds interest semiannually for 8 years, how many total
compound periods are there?

Question 59

Add the polynomials.

Question 60

Multiply the polynomials. $$( 3.4 a + 7 ) ( 0.5 a - 9 )$$

A) $1.7 a ^ { 2 } - 27.1 a - 63$
B) $1.7 a ^ { 2 } - 3.5 a - 4.5$
C) $3.9 a - 63$
D) $1.7 a ^ { 2 } - 63$

Question 61

Determine whether x and y vary directly, inversely, or jointly in the following equation.

Question 62

Multiply the polynomials.

Question 63

Add the polynomials.

Question 64

$2500 is borrowed from a bank that charges 10% simple interest. If the money is repaid in 5 1/2 years, how much must be paid back?

A) $3885
B) $3865
C) $3875
D) $3855

Question 65

Factor completely.

Question 66

Simplify the expression. Write the answer in exponent form.

Question 67

Identify a and determine if the parabola opens upward or downward.

Question 68

Factor the binomial completely.

Question 69

Subtract the polynomials.

Question 70

Multiply the polynomials.

Question 71

Simplify.

A)
B)
C)
D)

Question 72

Factor completely.

A)
B)
C)
D)

Question 73

Apply the distributive property.

Question 74

Factor completely.

Question 75

Evaluate the expression by using a calculator.

Question 76

Simplify.

Question 77

Simplify.

Question 78

The population of bacteria culture was 2000 at noon, and was increasing at a rate of 10 % per hour. The number of bacteria can be found using the function
where t is the number of hours past noon. Predict the population 9 hours later, at 9 PM to the nearest whole number.

A) 6736
B) 19,800
C) 4716
D) 2716

Question 79

Factor the polynomial completely.

Question 80

Use the distance formula to find the distance between the two points.