Question

Is the function `y=-8\left(2\right)^{x}` a growth because

Answer 1

The function y=-8
`(2)^x` represents exponential decay, not growth, because the coefficient -8 is negative. As x increases, the values of y become more negative, indicating decay rather than growth.

The function y=-8(2)^x is not a growth function, but rather a decay function. In general, for a function of the form y=
`ab^x`, if a > 0 and 0 < b < 1, it represents exponential decay; if a > 0 and b > 1 it represents exponential growth.

However, if a < 0, the function represents exponential decay, regardless of the value of b, because the negative sign causes the output values to be negative as x increases.

Therefore, since -8 is negative and 2 is greater than 1, the function -8
`(2)^x` will get more negative as x increases, indicating decay.

To further understand this, consider x=1 and x=2.

For x=1, y=-8
`(2)^1`=-16, and

for x=2, y=-8
`(2)^2`=-32.

The values of y become more negative as x increases, confirming that the function represents exponential decay, not growth.