your mathmatics instructor askes you to graph f(x)=2^x between 0 and 40, using as scale of 10 units per inch, what are the dimentions on the sheet of paper needed to draw this graph?

To determine the dimensions of the sheet of paper needed to draw the graph of f(x) = 2^x between 0 and 40, with a scale of 10 units per inch, we need to find the total length and width required.

1. Determine the length:
Since the graph is plotted from x = 0 to x = 40, we need to find the total length of the x-axis. Given that the scale is 10 units per inch, we divide the total length by the scale to get the length in inches.
Total length = 40 units
Length in inches = 40 units / 10 units per inch
Length in inches = 4 inches

2. Determine the width:
To plot the y-axis, we need to identify the maximum y-value of the function, which is f(40). Calculate f(40) as follows:
f(x) = 2^x
f(40) = 2^40
f(40) is a very large number, but let's approximate it.
Using a calculator or computer, we find f(40) is approximately 1.0995116 × 10^12.

Now, we need to determine the scale on the y-axis. Since it has not been provided in the question, we will assume the same scale of 10 units per inch, similar to the x-axis.

Divide the y-value by the scale to obtain the width in inches:
Width in inches = f(40) / 10 units per inch
Width in inches = 1.1 × 10^12 / 10
Width in inches = 1.1 × 10^11 inches

Therefore, the dimensions of the sheet of paper needed to draw this graph would be approximately 4 inches by 1.1 × 10^11 inches.