The increase in the number of humans living on Earth (N, as measured in billions) with time t (as measured in years since 1800) is modeld by the following function: N = 0.892e^0.00910t. If you were to graph in (N) versus t, what would be the slope of the line?

If we use the logarithmic scale on the y-axis, the slope would be 0.00919

Here we know that N(t) is an exponential equation, but we want to get a line when we graph it, so what we should do is a change of scale.

Remember that:

Ln(e^x) = x

So, if we use the logarithmic scale in the y-axis (this means that we are actually graphing Ln(N(t)), but this is allowed) we will get:

Ln(0.892e^0.00910t)

Now remember that:

Ln(A) + Ln(B) = Ln(A*B)

Then:

Ln(0.892e^0.00910t)  = Ln(0.892) + Ln(e^0.00919*t)

Ln(N(t)) = -0.114 + 0.00919*t

You can see that this is now a linear relation, and you can see that the slope is 0.00919

If you want to learn more about the logarithmic scale, you can read:

link

The slope of the line would be 0.00910 in a logarithm graphic.

Step-by-step explanation:

Statement is incomplete. The correct sentences are: The increase in the number of humans living on Earth (N, as measured in billions) with time t (as measured in years since 1800) is modeld by the following function: N = 0.892e^0.00910t. If you were to graph in ln (N) versus t, what would be the slope of the line?

Let be , where is the number of humans living on Earth, measured in billions, and is the time, measured in years since 1800. As we notice, this is an exponential function and its slope is not constant and such expression have to be linearized by using a logartihm graphic. We add logarithms on each side of the formula and simplify the resulting expression by means of logarithmic properties:

In a nutshell, the slope of the line would be 0.00910 in a logarithm graphic.

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step-by-step explanation:

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