Final answer:
To find the exponential equation of the form y = ab^x that passes through the points (-5,3) and (4,1), we create a system of equations based on these points and solve for a and b. The final exponential function is found by substituting the value of b back into one of the equations to solve for a.
Step-by-step explanation:
The question asks for an exponential equation that passes through the points (-5,3) and (4,1). To find such an equation of the form y = ab^x, we can use the given points to form two equations and solve for the values of a and b.
Using the point (-5,3), we get the equation 3 = a * b^(-5). Using the point (4,1), we get the equation 1 = a * b^4. Now we have a system of two equations with two unknowns:
- 3 = a * b^(-5)
- 1 = a * b^4
Dividing the second equation by the first one gives b^9 = 1/3. Taking the ninth root of both sides, we find that b = (1/3)^(1/9). Plugging this value of b back into the first equation allows us to find the value of a, which gives us the final exponential function that passes through the given points.