Mathematics, 04.07.2020 22:01 kimberlyhansen92

Determine the explicit form of the function that describes the sequence below. 16, 24, 36, 54, ...

A. f(n) = 8n + 8
B. f(n) = 16(3/2)^(n - 1)
C. f(n) = 3/2(n - 1) + 16
D. f(n) = 3/2(16)^(n - 1)

Answers: 3

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Answer from: kingbob101

B. f(n) = 16(3/2)^(n - 1).

Step-by-step explanation:

You can just substitute values. For questions like these, I usually use the second or third value to try the equations, because most of the time, the people who made these problems would make them all work for the first or last values.

A: 8n + 8 = 8 * 3 + 8 = 24 + 8 = 32. 32 is not equal to 36, so you can eliminate A.

B: 16 (3/2)^ (n - 1) = 16 * (1.5)^ (3 - 1) = 16 * (1.5)^ 2 = 16 * 2.25 = 36. 36 = 36, so you can keep this choice... for now.

C: 3/2 (n - 1) + 16 = 1.5 * (3 - 1) + 16 = 1.5 * 2 + 16 = 3 + 16 = 19. 19 does not equal 36, so you can eliminate C.

D: 3/2 (16)^ (n - 1) = 1.5 * (16)^ (3 - 1) = 1.5 * 16^2 = 1.5 * 256 = 384. 384 does not equal 36, so you can eliminate D as well.

Since A, C, and D do not work, you can say that the explicit form of the function would be Choice B.

Just to be sure, you can check using all four values...

f(1) = 16 * (1.5)^0 = 16 * 1 = 16 TRUE

f(2) = 16 * (1.5)^1 = 16 * 1.5 = 24 TRUE

f(3) = 16 * (1.5)^2 = 16 * 2.25 = 36 TRUE

f(4) = 16 * (1.5)^3 = 16 * 3.375 = 54 TRUE

Since all of the values match up, you can be sure that Choice B is the right answer.

Hope this helps! :)

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

Answer from: Quest

$85420 \times 0.6\%$

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