Final answer:
The exponential equation is found by using the points (7, 19) and (10, 31) and the form y = ab^x. After setting the points into the equation and solving for constants a and b, the specific exponential equation can be written, but a numerical solution requires further computation.
Step-by-step explanation:
To find an exponential equation given two points, we first need to determine the form of the equation, which is generally y = ab^x, where a is the initial value, b is the base or the growth rate, and x is the exponent or the independent variable.
Given the points (7, 19) and (10, 31), we can set up two equations where a and b are constants that we need to find:
- 19 = a * b^7
- 31 = a * b^10
Divide the second equation by the first to eliminate a and solve for b:
- 31/19 = b^10/b^7
- 31/19 = b^3
- b = (31/19)^(1/3)
Then, we can solve for a using one of the original equations:
- 19 = a * (31/19)^(7/3)
- a = 19 / (31/19)^(7/3)
Once we have the value of a and b, we write the exponential equation in the form y = ab^x. However, a numerical solution for a and b should be computed.