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.