Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

In this problem, we are going to answer the following question. Given two points (1,1) and (2,2), can we find an exponential function y

image text in transcribed 

In this problem, we are going to answer the following question. Given two points (1,1) and (2,2), can we find an exponential function y = c(a), such that it passes through both of these points? If so, how many such functions can we find? a. Let us for example, take an arbitrary two points (3, 16) and (2,8). If there is an expo- nential function y = c(a)" which passes through these two points then r = 3, y = 8 and x=2, y = 4 must satisfy the equation. So we have 16 = c(a) 8 = c(a) For some constants a, c. Our goal is to find these constants. First find a and then by using a find c. Hint: Try to divide both the equations and use the law of exponents. If we found those then we have the equation y = c(a)*. b. Can there be any other exponential function that has different a and c values we obtained in (a) to satisfy the above condition (i.e passes through the two points (3, 16) and (2,8))? Why or why not? Give reasoning. c. Now let us take another set of two points, (-2,24) and (1,3). Follow the direction as in (a) to find the equation of the exponential function which passes through these two points. d. Now let us take another set of two points (2,8) and (-2, -8). Follow the direction as in (a) to find the equation of the exponential function which passes through these two points. Could we find an equation? Why or why not? Give reasoning. Hint: In an exponential function y = c(a) can a take a negative value? e. Now try to generalize what we found in this problem and come up with an answer to our original question: Given two points (1, 1) and (2, 2), can we find an exponential function y = c(a), such that it passes through both of these points? And under what conditions can the answer be "yes" to the above question?

Step by Step Solution

3.47 Rating (157 Votes )

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Probability and Random Processes With Applications to Signal Processing and Communications

Authors: Scott Miller, Donald Childers

2nd edition

123869811, 978-0121726515, 121726517, 978-0130200716, 978-0123869814

More Books

Students also viewed these Mathematics questions