Write the equation for an exponential function that

Question

Has a base of 3; has been stretched vertically by a factor of 2/3. reflected in the

y-axis; has an asymptote of y = 2 and passes through the point (0, 3. 5)

Answer 1

y=a(3)^-x + 2

adding 2 makes the asymptote y=2

negative x reflects it around the y axis

stretch (compress) by factor of 2/3

y=(2a/3) (3)^(-x) + 2

through the point (0,3.5)

3.5 = 2a/3 +2

2a/3 = 1.5

a = 1.5/(2/3) = 9/4

y = (2/3)(9/4)(3^-x) + 2

y =(3/2)3^-x +2

y=(1/2)(3)(3^-x) + 2

y = 0.5(3)^(1-x) + 2

y = (0.5)3^1-x + 2

it may help to draw a rough sketch

graphically, the y intercept is 3.5. there are no x intercepts

as x approaches infinity, y approaches 2

as x approaches negative infinity, y approaches infinity