Days Passed (x) Letters Received (y) 0 1 1 5 2 25 3 125 4 625 5 3125 6 15,625 7
ID: 3079749 • Letter: D
Question
Days Passed (x) Letters Received (y) 0 1 1 5 2 25 3 125 4 625 5 3125 6 15,625 7 78,125 8 390,625 Activity Sheet 15.1 1. (15.1, #1) Write a function in y = a*bx form that represents the pattern shown in the table. That is, determine numerical values for a and b, and write an exponential function. 2. Provide a graph that shows both the data provided in the table and your function on a reasonable viewing window. Your function should pass through the data points. 3. (15.1, #2) On what day will 1 million people receive a copy of the letter? Explain.Explanation / Answer
f(x) = abx
f(0) = 1 bx = 0
f(1) = 5 = 51
f(2) = 25 = 52
f(3) = 125 = 53
The y-values look like powers of 5. If that's so, then
a = 5
b = 1
Evaluate the f(x) = 5x from 4 to 8 to see if all given points are (n, 5n).
f(4) = 54 = 625
f(5) = 55 = 3125
f(6) = 56 = 15625
f(7) = 57 = 78125
f(8) = 58 = 390625
Solve part 3 either by trial and error or by evaluating log51000000
f(9) = 59 = 1,953,125 A million people receive the letter on the ninth day. Although the volume is nearly two million, day 9 is the first day that at least one million people receive the letter.
Insert drawing does not work. Evaluating y = 5x on a TI-83 Plus showed an exponential function.
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