Find a formula for the exponential function passing through the points (-1, '3' y = acer and (1,12)

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The formula is y=     the right answer is not f(×)=

**Finding the Exponential Function**

**Objective:** To find a formula for the exponential function passing through the given points (-1, 4/3) and (1, 12).

Given the following points:
- (-1, 4/3)
- (1, 12)

We need to determine the exponential function y = ab^x.

The task involves identifying the values of 'a' and 'b' such that the given exponential function passes through the specified points. Use these points in the exponential formula to create equations and solve for 'a' and 'b'. Enter the simplified formula in the designated box.

**Step-by-Step Solution:**

1. Insert each point into the general form of an exponential function \( y = ab^x \).
2. Form two separate equations based on these points.
3. Solve these simultaneous equations to determine the values of 'a' and 'b'.

**Note:**
- Substitution and algebraic manipulation are essential steps in reaching the solution.
- After solving for 'a' and 'b', recheck using the given points to ensure the accuracy of the derived exponential function.

**Your Answer:**
- Fill in the box with the simplified form of the exponential function once you determine it from the steps above.

y = _______
Transcribed Image Text:**Finding the Exponential Function** **Objective:** To find a formula for the exponential function passing through the given points (-1, 4/3) and (1, 12). Given the following points: - (-1, 4/3) - (1, 12) We need to determine the exponential function y = ab^x. The task involves identifying the values of 'a' and 'b' such that the given exponential function passes through the specified points. Use these points in the exponential formula to create equations and solve for 'a' and 'b'. Enter the simplified formula in the designated box. **Step-by-Step Solution:** 1. Insert each point into the general form of an exponential function \( y = ab^x \). 2. Form two separate equations based on these points. 3. Solve these simultaneous equations to determine the values of 'a' and 'b'. **Note:** - Substitution and algebraic manipulation are essential steps in reaching the solution. - After solving for 'a' and 'b', recheck using the given points to ensure the accuracy of the derived exponential function. **Your Answer:** - Fill in the box with the simplified form of the exponential function once you determine it from the steps above. y = _______
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