x lnx 1x or x2 and y lny 1y or y2 You have the following dat

x, lnx, 1/x, or x^2 and y, lny, 1/y, or y^2

You have the following data points which belong to a function of the form y = ae^bx, where b can be positive or negative. You wish to determine the value of the constant, b, and to do so you will construct a linear plot. What will you plot against what? y-axis label: x-axis label: From the values of x and y in the table above, calculate the values of the three corresponding data points. Use the points to graph the function on the grid below. Use \"New curve by table points\" on the left-hand side of the graph; line segments will automatically connect the points. Enter the x-axis values in the x column and the y-axis values in the f(x) column. What is the numerical value of the constant, b?

Solution

y = ae^bx

taking ln (log to the base e) on both sides, we get:

ln(y) = ln(ae^bx)

=> ln(y) = ln(a) + ln(e^bx)

=> ln(y) = c + bx

this is of the form y = mx + c

therefore, plot ln(y) on the y axis and x on the x axis.

The slope of the obtained graph will be the value of b.

for 1st: value: ln(4.73) = c + (0.1b)

=> c = 1.554 - 0.1b ...............................[1]

and for the 2nd value, ln(7.6) = c + (0.2b)

=> c = 2.028 - 0.2b ..............................[2]

equating equations [1] and [2], we get:

1.554 - 0.1b = 2.028 - 0.2b

=> b = 4.74.