Question

Write an equation of an exponential function of the form y=ab^x passing through the points (0,8) and (6,0.125)

Answer 1

Answer:

$y=8\cdot \left(\dfrac{1}{2}\right)^x.$

Step-by-step explanation:

If the graph of exponential function passes through the points (0,8) and (6,0.125), then the coordinates of these points sutisfy the equation $y=a\cdot b^x:$

$8=a\cdot b^0\Rightarrow a=8,\\ \\0.125=8\cdot b^6\Rightarrow \dfrac{1}{8}=8\cdot b^6,\\ \\b^6=\dfrac{1}{64},\\ \\b^6=\dfrac{1}{2^6}\Rightarrow b=\dfrac{1}{2}.$

Thus, the equation of exponential function is

$y=8\cdot \left(\dfrac{1}{2}\right)^x.$