Thursday,+February+4,+2010Set3

Link to worksheet is right here:

problem 1 Davis An exponential function doesn't have a steady slope. therefore when a person is looking at an exponential equation that has been graphed, it should always have a slight curve to it, which can't be removed by adjusting the window. And your friend should know this also! What is he/she doing wrong? How is the calculator interpreting what he/she typed in?

problem 3 Erica The function f(x)=a^x is an exponential function in which a>1. Here, I've used 2 to demonstrate. The graph is a "j-shaped curve", one in which the function becomes infinitely close to the x-axis but never touches it on one end, and on the other it becomes exponentially larger. The other function, g(x)=b^x, has a value where 0<b<1. The fraction that I chose to represent this was 1/2. From the graph, it is obvious that the two functions have the same shape but have been reflected over the y-axis. The shape of each function is identical, but the direction is opposite. Good, clear explanation!! The graph helps a lot!

problem 4 Carly---

problem 5a James f(x)=3(5)^x

problem 5b Austin I actually got a different answer for "a" f(x)=-48(1/2)^x problem 5c Nico I actually got a different answer completely. I could be wrong, but I got y = 2 * 4^x f(x)=4(1/4)^x problem 6 Jeff Good! The two points given are the Y intercept (0,1) and (2,100) I used the process of y = a(b^x) Then I plugged in for a,x, and y and then solved for b.

problem 7 Jesse I used y=ab^x y=1/16 x=4 a=1 1/16=1×b^4 1/16=b^4 1/2^4=b

problem 8 Zander Cannot solve, the question is incomplete (only one point is showing).

problem 9 Danny Good! There is first a given point on the Y intercept, (0,1.2). since a in the equation is the initial point, a=1.2 y=1.2*b^x 4.8=1.2(b)^2 4.8/1.2=4 4=b^2 b=2 so the equation is y=1.2*2^x

problem 10 Ryan (Same as Danny's) But what you want to try and do is find the values to plug into the equation y=a*b^x In this equation a is the initial point and is the y intercept Y is the y value of one of the coordinates on the line X is the x value of the same coordinate Now you are able to solve for the b variable and know the entire equation Look above at Danny's Equation

problem 11 Lacey The function f(x) is linear because the rate of change is constant. The equation is f(x)= 0.87965x-2.19912 The function g(x) is not linear, and therefore exponential, because the rate of change is not constant. (I had some trouble figuring out the exponential pattern for the y value.) The equation is g(x)=1.25663 * 1.10610^x The function h(x) is also exponential because the rate of change is not constant. Sorry, I still can't figure out what the exponential pattern is! This is a difficult one -- my conclusion was that it was linear-ish, with equation y = 0.92814x + 2.19912 The equation is h(x)=2.82743 * 1.33469^x

problem 12 Hannah I estimate a as 12 and b as 1/1.2 by using the first two points in the table. Based on plugging in the values for a and b into other points in the table, I realize that it is reasonable but not great. For example, when I plugged it in with the time of 5.0, using the a and b values, I got 4.8 for the concentration, which is a little bit off.

problem 13 Laura No, it cannot be exponential. Why not? I actually thought that it was...even came up with a nice equation. Observe the fact that at some point x goes from 2 to 4 rather than 2 to 3, and 5 to 8 rather than 5 to 6.