Question

I need the answers for 6 and 7. Attached below is my work for 1-5. Thank you.

My work:

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) fromx - 0 tox -0.1, so that Ax -0.1. Recall that the average rate of change is Show your steps and write your Δι answer on the first line of the table below. (5) 2. Continue finding the average rate of change using 0 as your initial x-value and letting get smaller. Write the results in the table below and copy to your paper. Interval 0, 0.1 0, 0.01 0, 0.001 0, 0.00011 0.0001 Average rate of change 0.01 0.001 (2) 3. Using your observations from the table, complete this sentence on your paper: As Ax gets smaller and smaller, gets (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: A:s Ar gets smaller and smaller, ge (596. For both functions it seems that as ΔΧ 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. 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 (5) 7. nster he sallauin Chon The objeu.ve i to ithe auncae cotegefram Xz0 tO Usng Average ate of change- Au cont of chan af chenge faimula the arerage sate gt -ㄧ αλ..to 1011713-1 0,1 0.0 ComQure he Sallau ma tode usnthe mevels rnd ar -0,01 L 00495350-1 0.65555 0 6956 0,6934 and 0a3 respecvely Compure the falaang table e T9llawna tahle ve e fate of change 0.31S 9,65 6 Ф.6934 0.01 0, 001 0,0,00 ,0.000.000 06 the table, complcse thy sen tence on o 161 0,0 0,0,00 0.0o し0986 xia

Answer 1

Tor the funchon f(x)- (2.5 = 0.3515 -(2-5) o. o (25) 二0-3205 ncion On Co, o.1 자 1.0844. 41 - 1:0245 I 、 On Lo, 0 00( On LO, o.oooL] 스ナ = 1,0301 ーー)-02.9 6. For the funcHon f(x)= (2-7) On [0, o.1.J 씌: 1.04425 On LO, o.01 On [o , О.oo 1.J Ay o..gg37 A 0.9333 So for a value co hichjn closeto 2.7 ノwe 7) The valau- which n close. to 2.3イ must be ethe average rute of chan a ve γα3c for fx et, the on the inkrva