AnswersCMS 2026-2027 NC Math 3 CREDIT RECOVERYExponential and Logarithmic Functions

Practice Test Answers

11 verified answers
1
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The two expressions have the same value when rounded to the nearest hundredth. the log base 5 of b the log base 9 of 48 What is the approximate value of log b to the nearest hundredth?

A
1 point 2 3
B
65 point 5 3
C
9 point 1 6
D
0 point 9 3
3
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What is the range of the function f of x is equal to negative 2 times open paren 6 to the x th power close paren plus 3 ?

A
left bracket 3 comma infinity right parenthesis
B
open paren negative infinity comma 3 close paren
C
left bracket negative 2 comma infinity right parenthesis
D
left parenthesis negative infinity comma negative 2 right bracket
4

For what value of x does 625 is equal to 5 raised to the 6 minus 2 x power ?

A
1
B
2
C
5
D
4
5

A customer deposits 1 dollars comma 000 in an account in which the interest is compounded annually. The table shows the balances in the account at the end of each year. Amount in Account vs. Number of Years Amount in Account, cap A Number of Years After Initial Deposit, t 1 comma 000 0 1 comma 080 1 1 comma 166 point 4 0 2 1 comma 259 point 7 1 3 1 comma 360 point 4 9 4 Which equation best represents the data in the table?

A
cap A is equal to 1000 times 1 point 0 8 to the t th power
B
cap A is equal to 1000 times 1 point 8 to the t th power
C
cap A is equal to 1080 to the t th power
D
cap A is equal to 800 to the t th power
6

If 343 to the x th power is equal to 49 raised to the 4 minus x power , what is the value of x ?

A
2
B
5 eighths
C
8 fifths
D
8
7

A customer deposits 500 dollars in an account that pays 4 percent annual interest. What is the balance after 3 years if the interest is compounded annually? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t = years since initial deposit n = number of times compounded per year r = annual interest rate (as a decimal) cap p = initial (principal) investment cap v times t = value of investment after t years

A
512 point 0 0 dollars
B
500 point 1 2 dollars
C
562 point 4 3 dollars
D
560 point 0 0 dollars
8

Which graph shows the solution to the equation? log sub 3 of open paren x plus 2 close paren is equal to 1

A
Image with description Coordinate plane with x-axis and y-axis. A logarithmic-shaped curve begins near the y-axis at x equals 0 and extends to the right. The curve passes through 1 comma 0, rises gradually through approximately 3 comma 1 and 9 comma 2, and continues increasing as x increases. A horizontal line y equals negative 1 extends across the graph with arrows on both ends. The curve intersects the horizontal line near 0.3 comma negative 1 and lies above the line for x values greater than this point. Both the curve and the horizontal line continue indefinitely as indicated by arrows.
B
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (1 comma 1) and increases as x increases. There is a line parallel to the x axis and cuts the y axis at (0 comma 1).
C
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma negative 1).
D
Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma 1).
9

The intensity, or loudness, of a sound can be measured in decibels d cap b , according to the equation cap i times d cap b is equal to 10 log open bracket the fraction with numerator cap i and denominator cap i sub 0 close bracket , where cap i is the intensity of a given sound and cap i sub 0 is the threshold of hearing intensity. What is the intensity, in decibels, open bracket cap i times d cap b close bracket , when cap i is equal to 10 to the 32th power times open paren cap i sub 0 close paren ?

A
15
B
737
C
320
D
32
10

Which function has a horizontal asymptote of y is equal to 3 ?

A
f of x is equal to 2 times open paren 4 to the x th power close paren plus 3
B
f of x is equal to 2 times open paren 3 to the x th power close paren
C
f of x is equal to 2 times 4 raised to the x minus 3 power
D
f of x is equal to 3 times open paren 2 to the x th power close paren
11

What is the solution of the log base x of 729 is equal to 3 ?

A
18
B
81
C
6
D
9
12

What is the solution of the natural log of open paren x plus 6 close paren minus natural log 9 is equal to 2 ? Round your answer to the nearest hundredth.

A
x is equal to 60 point 5 0
B
x is equal to 72 point 5 0
C
x is equal to 66 point 5 0
D
x is equal to 53 point 5 0

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