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

Do you have the time to do it analytically?

Form of exponential equation you desire: y = a * b^(x),

where "a" and "b" are unknown values which we will calculate from a system of two equation based on your Cartesian (x, y) coordinate points.

System of equations:

Equation 1: 8 = a * b^(4) ... from the point: (4, 8)

Equation 2: 32 = a * b^(6) ... from the point: (6, 32)

# I arbitrarily labeled the equations, so we can know what's what. I would recommend canceling out variable "a: by dividing the equations like so ... Equation 2 ÷ Equation 1 = ???

# If you do it the other way, you will have to resolve a negative exponent on the "b" variable.

32 / 8 = [a * b^(6)] / [a * b^(4)]

# Now, a's obviously cancel by division:

4 = b^(6 - 4) ... # simplifying exponents:

4 = b^(2)

# Calculate the square root, to cancel the squaring:

±√4 = √[b^(2)]

# We will just take the positive solution for "b". That will be good enough.

2 = b

# Now calculate variable "a" from either of the equations:

8 = a * b^(4) ... knowing the value of "b":

8 = a * (2)^(4)

8 = a * 16

# Now if you just divide both sides of the equation by 16, you get the reduced value of "a".

1 / 2 = a ... or 0.5 = a

Solution set: a = 0.5 ; b = 2

Exponential curve which fits the points: y = 0.5 * 2^(x)

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol