Which value of b in an exponential function will result in the percent rate of change given? 23% decrease b = 8% increase b = 15% decrease b = 120% increase b =

Given an exponential function of the form

y = a*(b)^x

The values of b that will result in the desired percentage values are:

Case 1

b = 23% decrease

1 - 0.23 = 0.77

y = a*(0.77)^x

Case 2

b = 8% increase

1 + 0.08 = 1.08

y = a*(1.08)^x

Case 3

b = 15% decrease

1 - 0.15= 0.85

y = a*(0.85)^x

Case 4

b = 120% increase

1 + 1.2 = 2.2

y = a*(2.2)^x

See attached picture for examples

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.