when log s as ordinate is plotted against t as abscissa on l

when log s (as ordinate) is plotted against t (as abscissa) on linear paper, the graph is a straight line with slope of -2.1 and intercept of 1.5 . Express this relationship between s and t as s=bx^m. If s represents a distance in meters and t a time in seconds, what are the units of b and m? please show all steps

Solution

The equation of a straight in the xy plane with slope m and y-intercept c is y = mx+c.

When log s (as ordinate) is plotted against t (as abscissa) on linear paper, the graph is a straight line with slope of -2.1 and intercept of 1.5. Therefore, log s = -2.1 t +1.5. Hence s = 10^{(-2.1t +1.5)} = 10^1.5 10^-2.1t = bx^m where b = 10^1.5 , x = 10 and m = -2.1t