Question

Which is exponential?

a) 0
b) 1
c) 3
d) 4


y

a) 0
b) 1
c) 9
d) 16

х

o

N

a) 3
b) 4
c) 2
d) 5

у

a) 1
b) 3
c) 9
d) 27

х

a) 0
b) 1
c) 2
d) 3

у

a) 5
b) 2
c) 8
d) 16

Answer 1

The term exponential refers to a consistent multiplicative increase by a base number raised to increasing powers. In the options provided, the sequence (1, 3, 9, 27) is exponential because each term is 3 to the power of 0, 1, 2, and 3 respectively.

Step-by-step explanation:

The question appears to revolve around identifying an exponential sequence from given options. Exponential growth occurs when numbers increase by a constant factor in each step. That is, if the base is b, after n intervals, the amount will be b^n. Therefore, to find an exponential sequence, we look for a pattern where each term is a power of a base number.

Looking at the pairs given, (x,y) = (2, 4), (3, 9), (4, 16), we can identify that none are exponential sequences, as they do not show consistent multiplicative growth by the same factor.

However, when we look at the pairs (x, y) = (2, 4), (3, 9), (4, 16), they seem to be squares rather than exponential in the sense of growth by a fixed multiplier. The sequence (1, 3, 9, 27) does exhibit exponential characteristics as each term is 3 raised to an increasing power. When we apply the exponential arithmetic, we can confirm it: 3^0 = 1, 3^1 = 3, 3^2 = 9, and 3^3 = 27.