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 modeled by the following function: N=0.892e^0.00910t. If you were to graph ln(N) versus t, what would be the slope of the line? Report your answer using three significant figures.

Answer 1

The slope of the line when graphing ln(N) versus t is 0.00910.

Step-by-step explanation:

To find the slope of the graph of ln(N) versus t, we need to differentiate the given function. The derivative of ln(N) with respect to t can be found using the chain rule. Differentiating the function N=0.892e^(0.00910t) gives us dN/dt = 0.00910 * 0.892e^(0.00910t).

Next, we need to find the derivative of ln(N). Using the chain rule, we have d(ln(N))/dt = (1/N) * (dN/dt). Substituting the derivative we found earlier, we get d(ln(N))/dt = (0.00910 * 0.892e^(0.00910t)) / (0.892e^(0.00910t)). Simplifying further, we have d(ln(N))/dt = 0.00910.

Therefore, the slope of the line when graphing ln(N) versus t is 0.00910.

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