Math Problem Statement
Solution
To find the formula for the exponential function that passes through the points and , we can assume that the function has the form:
where and are constants. We will use the two points provided to solve for and .
Step 1: Use the Point
When , : Since , we get:
So, the equation becomes:
Step 2: Use the Point
When , :
Divide both sides by 4:
Take the square root of both sides to solve for :
Final Equation
Now we can substitute and back into the equation:
So, the exponential function that goes through the points and is:
Would you like more details, or do you have any questions?
Here are some related questions for further exploration:
- How do you determine if a function is exponential from a graph alone?
- What are other common forms of exponential functions?
- How would the equation change if was negative?
- How can you verify this function using additional points on the graph?
- What happens to the graph if the base is less than 1?
Tip: To find an exponential equation given two points, first use the -intercept (where ) to solve for the initial value , then use a second point to solve for the base .
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Algebra
Formulas
y = a * b^x
Theorems
-
Suitable Grade Level
Grades 9-12