Answers CMS 2026-2027 NC Math 3 CREDIT RECOVERYExponential and Logarithmic Functions

Exponential and Logarithmic Functions — Test Answers

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A factory produces 1 comma 250 comma 000 toys each year. The number of toys is expected to increase by about 150 percent per year. Which model can be used to find the number of toys, n (in millions), being produced in t years?

n is equal to 1 point 2 5 times 2 point 5 to the t th power

n is equal to 1 point 5 t plus 1 point 2 5

n is equal to 1 point 5 t squared plus 1 point 2 5

n is equal to the fraction with numerator 2 point 5 times 1 point 5 and denominator t , t is not equal to 0

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If the equation is solved by graphing, which statement is true? the log of open paren 6 x plus 10 close paren is equal to the log base 1 half of x

The curves intersect at approximately x is equal to 0 point 7 5 .

The curves intersect at approximately x is equal to 3 point 0 7 .

The curves intersect at approximately x is equal to 0 point 4 6 .

The curves intersect at approximately x is equal to 1 point 1 1 .

For what value of n does the fraction with numerator 216 raised to the n minus 2 power and denominator open paren 1 over 36 close paren raised to the 3 n power is equal to 216 ?

negative 1 third

negative 3

5 ninths

If 1 over 64 is equal to 4 raised to the 2 s minus 1 power times 16 raised to the 2 s plus 2 power , what is the value of s ?

negative 1

no solution

Devon purchased a new car valued at 16 dollars comma 000 that depreciated continuously at a rate of 35 percent Its current value is 2 dollars comma 000 The equation 2 comma 000 is equal to 16 comma 000 times open paren 1 minus r close paren to the t th power represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

2 years

8 years

1 year

5 years

How does the value of log_2⁡100 compare with the value of the log base 6 of 20 ?

The value of the log base 2 of 100 is about 4 times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 1 third times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 3 times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 1 fourth times the value of the log base 6 of 20 .

What is the solution to the equation 2 raised to the x plus 4 power minus 12 is equal to 20 ?

x is equal to 1

x is equal to 9

x is equal to 0

x is equal to 2

What is the value of the log base 625 of 5 ?

negative 4

negative 1 fourth

1 fourth

For what value of n does open paren 1 over 36 close paren to the n th power is equal to 216 ?

3 halves

negative 3

negative 3 halves

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function f of t is equal to negative 16 t squared plus 48 t , where t is the time in seconds since the rocket was shot and f of t is the rocket’s height in feet. What is the maximum height the rocket reaches?

16 ft

144 ft

36 ft

48 ft

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 8th power times open paren cap i sub 0 close paren ?

For what value of x does 3 raised to the 4 x power is equal to 27 raised to the x minus 3 power ?

negative 9

negative 3

Which of the following shows the graph of y is equal to 4 to the x th power plus 3 ?

Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 0 as x approaches negative infinity, indicated by an arrow pointing left along the x-axis. The curve passes through the points (negative 3 comma 1), (negative 2 comma 4), and (negative 1 point 5 comma, 8). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.

Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals negative 3 as x approaches negative infinity, indicated by an arrow pointing left along the line y equals negative 3. It passes through the y-intercept (0 comma negative 2). The curve goes through the points (negative 1 comma negative 3), (1 comma 1) and (1 point 5 comma 6). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.

Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 3 as x approaches negative infinity. It passes through the points (negative 2 comma 3), (0 comma 4) and (1 comma 7). As x increases, the curve rises sharply towards positive infinity. As x decreases, the curve flattens out, approaching the asymptote at y equals 3.

Image with description On a coordinate plane, the x and y axes ranging from negative 10 to 10 in increments of 1 with major tick marks at even integers. A curve has a horizontal asymptote at y equals 0 as x approaches negative infinity, indicated by an arrow pointing left along the x-axis. It passes through the points (3 comma 1) and (4 comma 4). As x increases, the curve rises sharply towards positive infinity, indicated by an arrow pointing up and right.

Which graph shows the solution to the equation? the log base 3 of x is equal to the log base 0 point 5 of x

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. A straight line extends from a downward-pointing arrow near negative 5 comma negative 5, passes through 0 comma 0, and continues upward to an arrow near 5 comma 5. A curve extends from a downward-pointing arrow near 0 comma negative 5, increases upward to pass through 1 comma 0, and continues increasing to an arrow near 5 comma 1.5.

Image with description On a coordinate plane the x axis lists from negative 5 to 5 by 1 and y axis lists from negative 5 to 5 by 1. There is a curved graph that passes through (negative 4 comma negative 2), and (negative 2 comma negative 1). It increases in the third quadrant, changes direction at the origin, and then again increases in the first quadrant passing through (5 comma 1 point 5). There is line that passes through the origin, (1 comma 1), and (2 comma 2).

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. Four curves are plotted, with two entirely above the x-axis and two entirely below the x-axis. Above the x-axis, one curve extends from an arrow on the y-axis at 0 comma 0.5 up to an upward-pointing arrow near 1 comma 5, and a second curve extends from an upward-pointing arrow near 1 comma 5 down to an arrow near 5 comma 0.5. Below the x-axis, one curve extends from an arrow on the y-axis at 0 comma negative 0.5 down to a downward-pointing arrow near 1 comma negative 5, and a second curve extends from a downward-pointing arrow near 1 comma negative 5 up to an arrow near 5 comma negative 0.5.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both axes labeled from negative 5 to 5 in increments of 1 unit. Two curves intersect at 1 comma 0. The first curve extends from a downward-pointing arrow near 0 comma negative 5, increases upward to pass through 1 comma 0 and 3 comma 1, and continues increasing to an arrow near 5 comma 1.5. The second curve extends from an upward-pointing arrow near 0 comma 5, decreases downward to pass through 1 comma 0 and 2 comma negative 1, and continues decreasing to an arrow near 5 comma negative 2.5

Which graph represents an exponential decay function?

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at approximately (0 comma 0) and extends to the right in fourth quadrant. The curve is continuously decreasing and it passes through approximately (1 comma negative 1), (4 comma negative 2), and (9 point 5 comma negative 3).

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at the origin (0 comma 0) and extends into the first quadrant. The curve is continuously increasing and appears concave down. It passes through (1 comma 1), (3 comma 2), and (8 comma 3).

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), (0 comma 1), (1 comma 2), (2 comma 4) and (3 comma 8). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches negative infinity.

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 1 comma 2), (negative 2 comma 4), (negative 3 comma 8), (0 comma 1), (1 comma 0 point 5), and (2 comma 0 point 2 5). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches positive infinity.

A store uses the expression negative 2 p plus 50 to model the number of backpacks it sells per day, where the price, p , can be anywhere from 9 dollars to 15 dollars Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue is equal to price times number of backpacks.)

12 point 5 0 dollars per backpack gives the maximum revenue; the maximum revenue is 312 point 5 0 dollars .

9 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 32 point 0 0 .

15 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 20 point 0 0 dollars .

12 point 0 0 dollars per backpack gives the maximum revenue; the maximum revenue is 312 point 0 0 dollars .

What is the true solution to the given equation? 2 log sub 3 6 x minus log sub 3 of 4 x is equal to 2 log sub 3 open paren x plus 2 close paren

x is equal to negative 2 and x is equal to 1

x is equal to 2 and x is equal to 4

x is equal to 1 and x is equal to 4

x is equal to negative 2 and x is equal to 2

What is the approximate value of the log base 6 of 25 ?

1 point 7 9 6

0 point 2 3 3

0 point 6 2 0

0 point 5 5 7

The magnitude, cap m , of an earthquake is defined to be cap m is equal to the log of cap i over cap s , where cap i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and cap s is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

negative 0 point 5

1 point 5

negative 1 point 5

3 point 6

The range of which function is open paren 2 comma infinity close paren ?

y is equal to 2 to the x th power

y is equal to 2 times open paren 5 to the x th power close paren

y is equal to 5 to the x th power plus 2

y is equal to 5 raised to the x plus 2 power

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Exponential and Logarithmic Functions — Test Answers

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