What is the asymptote of y=4(0.5)^x
The asymptote of y=4(0.5)^x is y=0. This is because as x approaches infinity, (0.5)^x approaches 0, and 4 multiplied by 0 is still 0. Therefore, the curve approaches the x-axis but never touches it, creating a horizontal asymptote at y=0.
To find the asymptote of the function y = 4(0.5)^x, we need to consider the behavior of the function as x approaches positive or negative infinity.
As x approaches positive infinity, the term (0.5)^x approaches zero. Multiplying by 4, we still get a value close to zero. Therefore, as x approaches positive infinity, the value of y approaches zero.
As x approaches negative infinity, the term (0.5)^x also approaches zero. However, since we are multiplying this by 4, the value of y still approaches zero. Therefore, as x approaches negative infinity, the value of y also approaches zero.
Thus, the horizontal asymptote of y = 4(0.5)^x is y = 0.