Question

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?

Answer 1

Answer:

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 $N(t) = 0.892\cdot e^{0.00910\cdot t}$, where $N(t)$ is the number of humans living on Earth, measured in billions, and $t$ 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:

$\log N(t) = \log \left(0.892\cdot e^{0.00910\cdot t}\right)$

$\log N(t) = \log 0.892 + 0.00910\cdot t$

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

Answer 2

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

How to get a line when graphing an exponential equation?

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:

https://brainly.com/question/25867604