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

`y=8\cdot \left((1)/(2)\right)^x.`

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 (1)/(8)=8\cdot b^6,\\ \\b^6=(1)/(64),\\ \\b^6=(1)/(2^6)\Rightarrow b=(1)/(2).`

Thus, the equation of exponential function is

`y=8\cdot \left((1)/(2)\right)^x.`