Final answer:
To find an exponential function going through two points, we can set up a system of equations corresponding to the general exponential formula. Solving the system for the base and the coefficient gives us the specific function.
Step-by-step explanation:
The student is asking for the formula of an exponential equation that passes through two given points. To find this, we need to use the general form of an exponential function, which is f(x) = a * bx. Let's call the y-values from the points y1 and y2 and the x-values x1 and x2. So, we have the system of equations:
-
- y1 = a * bx1
-
- y2 = a * bx2
By plugging the points (-5, 3) and (4, 1) into these equations, we get:
-
- 3 = a * b-5
-
- 1 = a * b4
We now have two equations with two unknowns. To solve for a and b, we can use a system of equations. Dividing the second equation by the first equation allows for elimination of a and solving for b, and subsequently using the value of b to solve for a.
After finding a and b, we would have the specific exponential function that models the data given by the two points.