Determine which function(s) are exponential. Select all that apply.

The functions that are exponential would be:

B).   0          1          2         3           4

        1/3        1           3        9          27

C).       0          1          2         3           4

          5          5/2      5/4      5/8       5/16

What are Exponential Functions?

B). Given that,

  0          1          2         3           4

      1/3        1           3        9          27

As we see,

The value of undergoes a constant change of 1

The ratio also remains constant

Thus, it exemplifies an exponential function.

Similarly,

C).       0          1          2         3           4

          5          5/2      5/4      5/8       5/16

As we see,

The value of undergoes a constant change of 1

The ratio also remains constant

Thus, it exemplifies an exponential function.

Thus, options B and C are the correct answers as the other two have a constant change but not a constant ratio.

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option B and option C represent an exponential function.

Step-by-step explanation:

We know that following are some of the properties of different functions.

Linear Function:

The constant change in x and y

Quadratic Function:

The constant change in x

The constant 2nd differences in y

Exponential Function:

The constant change in x

The constant ratio in y

Determining the nature of the exponential function

Option A)

x       0          1          2         3           4

y       0          1           4         9          16

Here:

There is a constant change in x:

1 - 0 = 1;  2 - 1 = 1;  3 - 2 = 1;  4 - 3 = 1

BUT, there is NO CONSTANT ratio, as

1/0 = ∞,  4/1 = 4,  9/4 ; 16/9

Thus,

Table A DOES NOT represents an exponential function.

Option B)

x       0          1          2         3           4

y       1/3        1           3        9           27

Here:

There is a constant change in x:

1 - 0 = 1;  2 - 1 = 1;  3 - 2 = 1;  4 - 3 = 1

There is also a constant ratio, as

1/[1/3] = 3,  3/1 = 3,  9/3 = 3; 27/9 = 3

As there is constant change in x as well a constant ratio.

Thus,

Table B REPRESENTS an exponential function.

Option C)

x       0          1          2         3           4

y       5          5/2      5/4      5/8       5/16

Here:

There is a constant change in x:

1 - 0 = 1;  2 - 1 = 1;  3 - 2 = 1;  4 - 3 = 1

There is also a constant ratio, as

[5/2]/5= 1/2,

[5/4]/[5/2] = 1/2

[5/8]/[5/4] = 1/2

[5/16]/[5/8] = 1/2

As there is constant change in x as well a constant ratio.

Thus,

Table C REPRESENTS an exponential function.

Option D)

x       0          1          2         3           4

y       4.5       4        3.5       3          2.5

Here:

There is a constant change in x:

1 - 0 = 1;  2 - 1 = 1;  3 - 2 = 1;  4 - 3 = 1

BUT, there is NO CONSTANT ratio, as

4/4.5 = 4/[45/10] = 40/45 = 8/9

3.5/4 = [35/10]/4 = 35/40 = 7/8

3/3.5 = 3/[35/10] = 30/35 = 6/7

2.5/3 = [25/10]/3 = 25/30 = 5/6

Table D  DOES NOT represent an exponential function.

Conclusion:

Therefore, option B and option C represent an exponential function.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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