PART III Average rate of change of exponential functions near zero. (5) 1. Given f(x) =...
Fantastic news! We've Found the answer you've been seeking!
Question:
![image](https://dsd5zvtm8ll6.cloudfront.net/questions/2024/05/6641f4c384e19_5316641f4c314c9f.jpg)
Transcribed Image Text:
PART III Average rate of change of exponential functions near zero. (5) 1. Given f(x) = 2*, find the average rate of change of f(x) from x = 0 to x = 0.1, so that Ax = 0.1. Recall that the average rate of change is A. Show your steps and write your answer on the first line of the table below. Ax (5) 2. Continue finding the average rate of change using 0 as your initial x-value and letting Ax get smaller. Write the results in the table below and copy to your paper. Interval [0, 0.1] [0, 0.01] 0.1 0.01 [0, 0.001] 0.001 [[0, 0.0001] 0.0001 Average rate of change (2) 3. Using your observations from the table, complete this sentence on your paper: As Ax gets smaller and smaller, gets Ay Ax (5) 4. Make a similar table for g(x) = 3*, using the same intervals, and copy to your paper. (2) 5. Using your observations from this new table, complete this sentence on your paper: As Ay Ax Ax gets smaller and smaller, gets (5) 6. For both functions it seems that as Ax gets smaller, the average rate of change approaches a particular decimal. One of the decimals is greater than 1 and the other is less than 1. Using trial and error, try to find an exponential function whose average rate of change, using the same intervals as above, approaches 1. You should present at least 3 other exponential functions and their tables and each table should be accompanied by an observation similar to those in parts 3 and 5. (5) 7. Write your conjecture about the exponential function whose average rate of change on the interval [0, Ax], as Ax gets smaller and smaller, comes the closest to 1. PART III Average rate of change of exponential functions near zero. (5) 1. Given f(x) = 2*, find the average rate of change of f(x) from x = 0 to x = 0.1, so that Ax = 0.1. Recall that the average rate of change is A. Show your steps and write your answer on the first line of the table below. Ax (5) 2. Continue finding the average rate of change using 0 as your initial x-value and letting Ax get smaller. Write the results in the table below and copy to your paper. Interval [0, 0.1] [0, 0.01] 0.1 0.01 [0, 0.001] 0.001 [[0, 0.0001] 0.0001 Average rate of change (2) 3. Using your observations from the table, complete this sentence on your paper: As Ax gets smaller and smaller, gets Ay Ax (5) 4. Make a similar table for g(x) = 3*, using the same intervals, and copy to your paper. (2) 5. Using your observations from this new table, complete this sentence on your paper: As Ay Ax Ax gets smaller and smaller, gets (5) 6. For both functions it seems that as Ax gets smaller, the average rate of change approaches a particular decimal. One of the decimals is greater than 1 and the other is less than 1. Using trial and error, try to find an exponential function whose average rate of change, using the same intervals as above, approaches 1. You should present at least 3 other exponential functions and their tables and each table should be accompanied by an observation similar to those in parts 3 and 5. (5) 7. Write your conjecture about the exponential function whose average rate of change on the interval [0, Ax], as Ax gets smaller and smaller, comes the closest to 1.
Expert Answer:
Posted Date:
Students also viewed these mathematics questions
-
What is the most relevant measure of a company's profitability, the rate of return on assets or the rate of return on equity? Why? Which is the more meaningful measure of a company's profitability,...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
International Markets Project You have been hired as a globalization specialist by Kwik-E-Mart. Kwik-E-Mart is a large retailer that has outgrown its domestic market and seeks to expand its...
-
In its first month of operations, Rusch Company made three purchases of merchandise in the following sequence: (1) 300 units at $6, (2) 400 units at $7, and (3) 200 units at $8. Assuming there are...
-
b) If a company imported wine from France to sell in Australia, describe how its competitiveness is affected if the exchange rate of one Australian dollar to the Euro changed from 0.60 to 0.80.
-
In what ways do you think employing people of different ages, with different abilities and from a range of backgrounds and cultures could benefit your organisation and other organisations? Can you...
-
Write the PL/SQL code to create a procedure with only one IN parameter. Name the procedure as follows: -- The first 2 letters of the procedure name will have your INITIALS (in my case is NC) -- the...
-
What is the measurement of the feature at Maximum Material Condition (MMC) (listed first) and the positional tolerance zone at that measurement (listed second) on this drawing? Image Description: The...
-
Consider a monoatomic gas at STP whose N particles are confined to move only over a 2D square (rather than a 3D cube). The spectrum of these particles are given by = 2ma ;(n /2 + n) where m is the...
-
Consider a gas that obeys Bose-Einstein statistics, at a temperature below the Bose-Einstein condensation temperature TBE.
-
wlamart argues that it provides valuable jobs to small communities and should be allowed to grow. critics argue that these jobs are often low paying, with few benefits. what is your position? is a...
![Mobile App Logo](https://dsd5zvtm8ll6.cloudfront.net/includes/images/mobile/finalLogo.png)
Study smarter with the SolutionInn App