The variables x and y have an exponential relationship, one of the form y = Suppose that we also have the following table of values for x and y: We'll use these two data points to solve for C and a. Step 1: Solving for a. Point X y Point 1 2.7 27 Point 2 4.7 53 2 If we divide the equation y2 = Use the values from the table to make an equation involving only a: a = (Round these and all answers to 2 significant digits.) Solve this equation for a: Ca2 by the equation y₁ = Ca¹, we get the equation = a to the power Step 2: Solving for C. Substitute the value of a you found into the equation y₁ = = C. Solve this equation for C: C = = C.a. Y2 Y1 - x1 C. • a*¹ to get an equation involving only C:
The variables x and y have an exponential relationship, one of the form y = Suppose that we also have the following table of values for x and y: We'll use these two data points to solve for C and a. Step 1: Solving for a. Point X y Point 1 2.7 27 Point 2 4.7 53 2 If we divide the equation y2 = Use the values from the table to make an equation involving only a: a = (Round these and all answers to 2 significant digits.) Solve this equation for a: Ca2 by the equation y₁ = Ca¹, we get the equation = a to the power Step 2: Solving for C. Substitute the value of a you found into the equation y₁ = = C. Solve this equation for C: C = = C.a. Y2 Y1 - x1 C. • a*¹ to get an equation involving only C:
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. aª.
Suppose that we also have the following table of values for x and y:
We'll use these two data points to solve for C and a.
Step 1: Solving for a.
Point
X y
Point 1
2.7 27
Point 2 4.7 53
2
If we divide the equation y2
Use the values from the table to make an equation involving only a:
a =
=
Ca2 by the equation y₁
(Round these and all answers to 2 significant digits.)
Solve this equation for a:
= a to the power
Solve this equation for C:
C =
Step 2: Solving for C.
Substitute the value of a you found into the equation y₁
=
= C.
Y2
Ca¹, we get the equation = a
=
5
Y1
X2 -X1
Ca¹ to get an equation involving only C:
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