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.

$450.00 for 6 weeks

or

$300

step-by-step explanation:

$200.00 for first week $50.00 x5 equals $250 plus $200 equals $450.00 for six weeks.

$200 for first week

$200 x 0.10 = $20

$20 x 5 = $100

$200 + $100 = $300

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.