Answer:
[tex][/tex] You can follow these steps:
Step 1: Write down the general form of an exponential function:
The general form of an exponential function is: y = ab^x, where:
- "a" is the initial value or the value when x = 0.
- "b" is the base of the exponential function.
- "x" is the independent variable.
- "y" is the dependent variable.
Step 2: Use the given points to form a system of equations:
Given points are (2, 48) and (5, 750).
By substituting the x and y values of these points into the general form equation, we get two equations:
For point (2, 48): 48 = ab²
For point (5, 750): 750 = ab⁵
Step 3: Solve the system of equations to find the values of "a" and "b":
Now, we need to solve these two equations simultaneously to find the values of "a" and "b". You can use algebraic methods or software like a graphing calculator to find these values.
Step 4: Write the final equation:
Once you have found the values of a and b, you can substitute them back into the general form equation y = ab^x to get the specific equation for the exponential function.
Keep in mind that exponential functions grow quickly, so the values you calculated for "a" and "b" might be large.
I recommend using a graphing calculator or software to help you solve the system of equations efficiently and find the values of "a" and "b".
