Question

1.) Find an exponential function of the form y=ab^x whose graph passes through the points (2,48) and (5,3072)




2.) The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=3.

x=6, y=-1





3.) The variable z varies jointly with x and y. Use the given values to write an equation relating x, y, and z. Then find z when x =-2 and y=4.

x=1/3, y=3/4, z=5/2

Answer 1

#1
since y=ab^x, just plug in the two points you are given:

ab^2 = 48
ab^5 = 3072
Divide the 2nd by the first and you have
b^3 = 64
b = 4
a*4^2 = 48, so a = 3 and

y = 3*4^x

#2 inverse variation means xy = k, a constant. Plug in your values and you have

(6)(-1) = (3)(y)
y = -2

#3 direct variation means z = kxy
Or, z/xy = k, a constant. Plug in your values and you have

(5/2)/((1/3)(3/4)) = z/((-2)(4))
z = 80

Answer 2

You got z=80.. for some reason I got 10... can you check.