AnswersINMT3 Integrated Math 3 Sem 1 26-27Modeling with Quadratic Equations

Modeling with Quadratic Equations — Unit test Answers

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1
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Which of the following shows the graph of y = 4x + 3?

A
On a coordinate plane, an exponential function starts at y = 3 in quadrant 2 and then increases rapidly into quadrant 1.
Option A
B
On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly in quadrant 2.
Option B
C
On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly into quadrant 1.
Option C
D
On a coordinate plane, an exponential function starts at y = negative 3 in quadrant 3 and then increases rapidly into quadrant 1.
Option D
2
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Which function is shown in the graph below?

Question illustration
A
y = (one-half) Superscript x + 3 Baseline minus 1
Option A
B
y = (one-half) Superscript x minus 3 Baseline + 1
Option B
C
y = (one-half) Superscript x minus 1 Baseline + 3
Option C
D
y = (one-half) Superscript x + 1 Baseline minus 3
Option D
3

What is the solution to

Question illustration
A
x = negative 4
Option A
B
x = negative 2
Option B
C
x = 4
Option C
D
x = 8
Option D
4

What is the solution to the equation

Question illustration
A
mc012-2.jpg
Option A
B
mc012-3.jpg
Option B
C
mc012-4.jpg
Option C
D
mc012-5.jpg
Option D
5

A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

A
2.5 days
B
5.0 days
C
46.6 days
D
66.7 days
6

The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?Plant Heightt, time in monthsh, height in inches118218.21318.33418.42518.48618.54

A
10 months
B
14 months
C
16 months
D
28 months
7

What is the true solution to the logarithmic equation below?

Question illustration
A
x = 0
Option A
B
x = two-ninths
Option B
C
x = four-ninths
Option C
D
x = two-thirds
Option D
8

Which graph represents an exponential decay function?

A
On a coordinate plane, a curve opens up and to the right in quadrant 4.
Option A
B
On a coordinate plane, a curve opens up and to the right in quadrants 1 and 2. The line rapidly decreases in quadrant 2 and then curves and approaches the x-axis in quadrant 1.
Option B
C
On a coordinate plane, a line slightly curves up in quadrant 1.
Option C
D
On a coordinate plane, a line slowly increases in quadrant 2 and then increases rapidly into quadrant 1.
Option D
9

How does the value of compare with the value of ?

Question illustration
A
The value of is about 4 times the value of .
Option A
B
The value of is about times the value of .
Option B
C
The value of is about 3 times the value of .
Option C
D
The value of is about times the value of .
Option D
10

If the equation below is solved by graphing, which statement is true?

Question illustration
A
The curves intersect at approximately x = 0.46.
B
The curves intersect at approximately x = 0.75.
C
The curves intersect at approximately x = 1.11.
D
The curves intersect at approximately x = 3.07.
11

Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance, compounded annually. Which recursive formula represents the total amount of money in Victoria’s account at the end of the nth year?

A
mc023-1.jpg
Option A
B
mc023-2.jpg
Option B
C
mc023-3.jpg
Option C
D
mc023-4.jpg
Option D
12

Within the set of whole numbers, one set of numbers satisfies the recursive formula , when . What are the first two terms of the sequence?

Question illustration
A
3, 6
B
6, 30
C
2, 6
D
2, 3
13

If , what is the value of s?

Question illustration
A
–1
B
0
C
1
D
no solution
14

For what value of n does ?

Question illustration
A
–3
B
Negative one-third
Option B
C
Five-ninths
Option C
D
1
15

What is the range of the function

Question illustration
A
y less-than 0
Option A
B
y greater-than 0
Option B
C
y less-than 4
Option C
D
y greater-than 4
Option D
16

What is the domain of ?

Question illustration
A
all real numbers less than –3
B
all real numbers greater than –3
C
all real numbers less than 3
D
all real numbers greater than 3
17

Which of the following shows the extraneous solution to the logarithmic equation below?

Question illustration
A
x = negative 16
Option A
B
x = negative 8
Option B
C
x = negative 4
Option C
D
x = negative 2
Option D
18

What is the approximate value of ?

Question illustration
A
0.233
B
0.557
C
0.620
D
1.796
19

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

A
Makayla invests her money 1 year longer.
B
Makayla invests her money 2 years longer.
C
Calvin invests his money 1 year longer.
D
Calvin invests his money 2 years longer.
20

For what value of n does ?

Question illustration
A
–3
B
Negative three-halves
Option B
C
Three-halves
Option C
D
3

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