University:
University of Houston
Course:
MATH 3331 | Intermediate Differential Equations
Academic year:

2021
Views:

118

Pages:

5
Author:

Aldo Villarreal

Given a table of data that does not represent a linear function, we now ask: • How can we tell if the table represents an exponential function • If it does, how can we find a formula for the function Recognizing Exponential Data Given two points, the exponential growth or decay factor between them is given by: 1  y2 ( ∆x) a=   y1  For example, the exponential growth factor between (1, 2.8) & ( 4, 7.6832 ) is 1  7.6832  3 a =  = 1.4  2.8  To determine whether or not a table of data represents an exponential function, calculate the growth/decay factor between successive pairs of points. If this factor is “constant”, then the table represents an exponential function. Example 1 Determine whether or not the following tables represent exponential functions. For those that are exponential, give the growth factor. (a) x f(x) 0 64 3 32 6 16 9 8 (b) x f(x) 0 3.65 2 5.4327 3 6.6278 6 12.0352 (c) x f(x) 0 3.54 5 4.66 10 8.78 15 15.9 (d) x f(x) 2 5.046 4 10.6092 7 32.34352 Modeling Exponential Data Given that a table represents an exponential function, we construct the formula as follows: • the growth factor was determined in showing the table is exponential • the initial value may be given (the output for x = 0) or can be found by plugging any point in to the equation y = Pa x and solving for P Example 2 For each of the tables in example 1 that were exponential, construct the formula for the function. Example 3 Uranium-239 is an unstable isotope of uranium that decays rapidly. One gram of U239 was placed in a container, and the amount remaining was measured every 2 minutes. The data is shown below. (a) Show that the decay is exponential. 239 Tim U in (b) Give a formula for the amount of U239 remaining grams e after x minutes. 0 1 2 0.9428 6 0.83814 9 0.767314 (c) Use function notation to show the amount of U239 remaining after 10 minutes. (d) What is the half-life of U239?

Modeling Exponential Data

Related Documents

Recommended Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock