The variables and y have an exponential relationship, one of the form y=C.a². Suppose that we also have the following table of values for x and y: Point X Point 1 2.1 Point 2 6.1 We'll use these two data points to solve for C and a. Step 1: Solving for a. y 120 7500 If we divide the equation y2 = C. a2 by the equation y₁ = C. a¹, we get the equation =a²2-21 Use the values from the table to make an equation involving only a: = a to the power (Round these and all answers to 2 significant digits.) Solve this equation for a: a= C Y2 Step 2: Solving for C. Substitute the value of a you found into the equation y₁ = Ca¹ to get an equation involving only C: = C. Solve this equation for C: Y1
The variables and y have an exponential relationship, one of the form y=C.a². Suppose that we also have the following table of values for x and y: Point X Point 1 2.1 Point 2 6.1 We'll use these two data points to solve for C and a. Step 1: Solving for a. y 120 7500 If we divide the equation y2 = C. a2 by the equation y₁ = C. a¹, we get the equation =a²2-21 Use the values from the table to make an equation involving only a: = a to the power (Round these and all answers to 2 significant digits.) Solve this equation for a: a= C Y2 Step 2: Solving for C. Substitute the value of a you found into the equation y₁ = Ca¹ to get an equation involving only C: = C. Solve this equation for C: Y1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The variables x and y have an exponential relationship, one of the form y=C.a².
Suppose that we also have the following table of values for x and y:
Point X
Point 1
2.1
Point 2 6.1 7500
We'll use these two data points to solve for C and a.
Step 1: Solving for a.
a
If we divide the equation y2 = C a2 by the equation y₁ = Ca¹, we get the equation
Use the values from the table to make an equation involving only a:
= a to the power
(Round these and all answers to 2 significant digits.)
Solve this equation for a:
C
y
120
Step 2: Solving for C.
Substitute the value of a you found into the equation y₁ = Ca to get an equation involving only C:
Solve this equation for C:
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