"Look at this table: xy122438416532 Write a..." was answered by students like you

tinfoQ

Answered question

2020-11-27

Look at this table:

$\begin{array}{cc} x & y \\ 1 & 2 \\ 2 & 4 \\ 3 & 8 \\ 4 & 16 \\ 5 & 32 \end{array}$

Write a linear $(y = m x + b),$ quadratic $(y = a x 2)$ , or exponential $(y = a (b) x)$ function that models the data.

$y = ?$

Answer & Explanation

Alannej

Skilled2020-11-28Added 104 answers

The x-values are increasing by 1 each time and the y-values are doubling each time. Since the y-values are increasing by a constant factor of 2, the model must be exponential. The data would have to increase by a constant amount to be linear and the second difference of the y-values would have to be constant for the model to be quadratic.
Notice that each yy-coordinate is a power of 2. Since

2 = 2^{1}, 4 = 2^{2}, 8 = 2^{3}, 16 = 2^{4}

, and

32 = 2^{5}

, then each y-coordinate is a power of 2 where the exponent is the x-coordinate. The equation is then

y = 2^{x}

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