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

Answer:

$y=\frac{1}{2}(2)^x$

Step-by-step 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)

$\frac{32}{8}=\frac{b^6}{b^4}\\\\4=b^2\\\\b=\pm2$

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

$y=\frac{1}{2}(2)^x$