Question

Write an exponential equation in the form y = abx whose graph passes through points (4,8) and (6,32)

Answer 1

The general form of an exponential equation is given by:
y=abˣ
where:
a is the initial value and b is the growth factor.
From the points given (4,8) and (6,32), the growth factor will be:
b=(32)/(8)
b=32/8
b=4
hence
y=a4ˣ
the value a will be obtained by substituting the point (4,8) in the expression, thus
8=a4^4
8=256a
hence
a=8/256
a=1/32
hence the function will be:
y=1/32(4ˣ)

Answer 2

`y=(1)/(2)(2)^x`

Explanation:

The given equation is
`y=ab^x`

It passes through the points (4, 8) and (6, 32). Hence, we have

`8=ab^4.....(1)`

`32=ab^6.....(2)`

Divide equation (2) by (1)

`(32)/(8)=(b^6)/(b^4)\\\\4=b^2\\\\b=\pm2`

For b = 2

`8=a(2)^4\\\\8=16a\\\\a={1}{2}`

For b = -2

`8=a(-2)^4\\\\8=16a\\\\a={1}{2}`

Thus, the values of a and b are

a= 1/2, b = 2 and a= 1/2, b=-2

Thus, the exponential equation is

`y=(1)/(2)(2)^x`