Question

You have the following data points which belong to a function of the form y = aer, where b can be positive or negative. 4.10 0.100 3.32 0.200 2.69 0.300 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: 3-axis label: From the values of x and y in the table above, calculate the values of the three corresponding data points. Click on the graph below, and use the "Freeform Curves" tool to plot the data. Line segments will automatically connect the points. 10 anypononted Loan. This is one of 6 From the values of u and y in the table above, calculate the values of the three corresponding data points. Click on the graph below, and use the "Freeform Curves" tool to plot the data. Line segments will automatically connect the points. Enter Solution What is the numerical value of the constant, b? b=

Answer 1

To determine the value of b for a function y = ae^bx, apply a logarithmic transformation and plot ln(y) versus x. The b term is the y-intercept and the slope m determines the steepness of the line on a linear plot.

Step-by-step explanation:

To determine the value of the constant b for a function of the form y = aebx, you would need to create a linear plot by using a logarithmic transformation. This means you would plot the natural logarithm of y against x to create a linear relationship that will allow you to determine b. In the case of constructing a table similar to our function y = 9 + 3x, you would vary x, plug these values into the function, and calculate the corresponding y values. The y-intercept in this linear equation is denoted by the b term, which indicates where the line will intersect the y-axis when x equals zero. The slope m represents the change in y divided by the change in x, which gives the steepness of the line on the plot.

The provided data points do not directly correlate to this linear function as the functional form mentioned (y = aebx) suggests that the relation is exponential rather than linear. However, referring to the linear case, if b>0, the line slopes upward, if b=0 the line is horizontal, and if b<0, the line slopes downward.